Staff Selection Commission Mathematics - TIME AND WORK TYPE-I

Q.39

A and B together can dig a trench in 12 days, which A alone can dig in 28 days; B alone can dig it in

(1)20 days

(2)21 days

(3)22 days

(4)23 days

Ans .

(4)21 days

Explanation :
(2) B`s 1 days work = (A + B)s 1 days work - A`s 1 day`s work=\( \frac{1}{12} \)-\( \frac{1}{28} \)= \( \frac{7-3}{84} \)=\( \frac{4}{84} \)=\( \frac{1}{21} \). Required time = 21 days.

Q.40

A can complete a work in 'm' days and B can complete it in 'n' days. How many days will it take to complete the work if both A and B work together ?

(1) (m + n) days

(2)(\( \frac{1}{m} \)*\( \frac{1}{n} \))days

(3) (\( \frac{m+n}{mn} \))days

(4) (\( \frac{mn}{m+n} \)) days

Ans .

(4) (\( \frac{mn}{m+n} \)) days

Explanation :
4) A`s 1 days work =\( \frac{1}{m} \)and B`s 1 days work =\( \frac{1}{n} \)
(A + B)s 1 days work =\( \frac{1}{m} \)+\( \frac{1}{n} \)=\( \frac{n+m}{m} \)=\( \frac{m+n}{mn} \)
Required time = (\( \frac{mn}{m+n} \)) days

Q.41

Three men A. B and C working together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in

(1) \( \frac{2}{3} \)hour

(2)\( \frac{3}{4} \)hour

(3)\( \frac{3}{2} \)hour

(4) \( \frac{4}{3} \)hour

Ans .

(4) \( \frac{4}{3} \)hour

Explanation :
(4) Let A, B and C together do the work in x hours.
Time taken by A = (x + 6) hours Time taken by B= (x + 1) hours Time taken by C = 2x hours
=>\( \frac{1}{x+6} \)+\( \frac{1}{x+1} \)+\( \frac{1}{2x} \)=\( \frac{1}{x} \)
=>\( \frac{1}{x+6} \)+\( \frac{1}{x+1} \)=\( \frac{1}{x} \)-\( \frac{1}{2x} \)=\( \frac{1}{2x} \)
=>\( \frac{1}{x+6} \)=\( \frac{1}{2x} \)-\( \frac{1}{x+1} \)=\( \frac{x+1-2x}{2x(x+1)} \)
=>\( \frac{1}{x+6} \)=1-x/ 2x²+2x
=>2x ²+ 2x = x + 6 – x2 – 6x
=>3x ² + 7x – 6 = 0
=> 3x ² + 9x – 2x – 6 = 0
=> 3x (x + 3) – 2 (x + 3) = 0
=>(3x – 2) (x +3) = 0
=>3x – 2 = 0 as x + 3 != 0
=> x= \( \frac{2}{3} \)
Time taken by A =6+\( \frac{2}{3} \)=\( \frac{18+2}{3} \)=\( \frac{20}{3} \)hours
Time taken by B =1+\( \frac{2}{3} \)=\( \frac{5}{3} \)hours
(A +B)’s 1 hour’s work=\( \frac{3}{20} \)+\( \frac{5}{3} \)=\( \frac{3+12}{20} \)=\( \frac{15}{20} \)=\( \frac{3}{4} \)
Required time =\( \frac{4}{3} \)hour.

Q.42

A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is

(1) 100

(2) 96

(3) 95

(4) 90

Ans .

(2) 96

Explanation :
(2) Time taken by B and C = x days (let)
Time taken by A = 3x days
Part of work done by A, B and C in 1 day= \( \frac{1}{x} \) +\( \frac{1}{3x} \)=\( \frac{3+1}{3x} \)=\( \frac{4}{3x} \)
=> \( \frac{4}{3x} \)=\( \frac{1}{24} \) => 3x = 4 × 24
=> x= \( \frac{4*24}{3} \)=32days
Time taken by A = 32 × 3 = 96 days

Q.43

A can do a piece of work in 4 days and B can do it in 12 days. In how many days will they finish the work, both working together ?

(1) 4 days

(2) 6 days

(3) 2 days

(4) 3 days

Ans .

(4) 3 days

Explanation :
(3) (4) A`s 1 day`s work =\( \frac{1}{4} \)
B`s 1 days work = \( \frac{1}{12} \)
(A + B)s 1 days work =\( \frac{1}{4} \) +\( \frac{1}{12} \) =\( \frac{3+1}{12} \) =\( \frac{4}{12} \) =\( \frac{1}{3} \)
Required time = 3 days.

Q.44

A can do \( \frac{1}{4} \) of a work in 10 days. B can do \( \frac{1}{3} \)of the work in 20 days. In how many days can both A and B together do the work ?

(1) 30 days

(2) 32 days

(3) 24 days

(4) 25 days

Ans .

(3) 24 days

Explanation :
(3) A does \( \frac{1}{4} \) work in 10 days
A will do 1 work in 10 × 4 = 40 days
Similarly, B will do the same work in 20 × 3 = 60 days
(A + B)s 1 days work =\( \frac{1}{40} \)+\( \frac{1}{60} \) = \( \frac{3+2}{120} \)=\( \frac{5}{120} \) = \( \frac{1}{24} \)
Required time = 24 days .

Q.45

15 men take 20 days to complete a job working 8 hours a day. The number of hours a day should 20 men take to complete the job in 12 days

(1) 5 hours

(2)10 hours

(3)15hours

(4) 18 hours

Ans .

(2)10 hours

Explanation :
(2) Using Rule 1, M₁ D₁ T₁ = M₂D₂T₂
=>15 × 20 × 8 = 20 × 12 × T₂
=> T₂ = \( \frac{15*20*8}{20*12} \) =10 hours.

Q.46

Raj and Ram working together do a piece of work in 10 days. Raj alone can do it in 12 days. Ram alone will do the work in

(1) 20 days

(2) 40 days

(3) 50 days

(4) 60 days

Ans .

(4) 60 days

Explanation :
4) (Raj + Ram)s 1 days work =\( \frac{1}{10} \)
Raj`s 1 days work = \( \frac{1}{12} \)
Ram`s 1 day’s work = \( \frac{1}{10} \)-\( \frac{1}{12} \) = \( \frac{6-5}{60} \) = \( \frac{1}{60} \)
Required time = 60 days

Q.47

A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternately, with A beginning, then the work will be completed in

(1) 10 days

(2) 11 days

(3) 9 days

(4) 12 days

Ans .

(2) 11 days

Explanation :
(2) A`s 1 days work =\( \frac{1}{9} \)
B`s 1 days work = \( \frac{1}{15} \)
Work done in first 2 days = A`s 1 days work + B`s 1 days work = \( \frac{1}{9} \)+\( \frac{1}{15} \)= \( \frac{5+3}{45} \) = \( \frac{8}{45} \)
Work done in first 10 days = \( \frac{8*5}{45} \) =\( \frac{8}{9} \)
Remaining work = 1-\( \frac{8}{9} \) =\( \frac{1}{9} \)
Now, it is turn of 'A' for the eleventh day.
Time taken by 'A' in doing \( \frac{1}{9} \) work = \( \frac{1}{9} \) *9 = 1 day
Required time = 10 + 1 = 11 days.

Q.48

How many men need to be employed to complete a job in 5 days, if 15 men can complete \( \frac{1}{3} \) of the job in 7 days ?

(1) 20

(2) 21

(3) 45

(4) 63

Ans .

(4) 63

Explanation :
(4) Using Rule 1,
15 men complete \( \frac{1}{3} \)work in 7 days.
Time taken in doing 1 work = 3 × 7 = 21 days
=> M₁D = M₂D₂
=>15 × 21 = M₂ × 5
=>M₂= \( \frac{15*21}{5} \) = 63 days.s

Q.49

If x can finish a job in 4 hours and y can finish the same job in 8 hours independently, then they together will finish the job in

(1) 140 minutes

(2) 160 minutes

(3) 120 minutes

(4) 150 minutes

Ans .

(2) 160 minutes

Explanation :
(2) (x and y)s 1 hour work = \( \frac{1}{4} \) +\( \frac{1}{8} \) = \( \frac{2+1}{8} \) = \( \frac{3}{8} \)
Required time =\( \frac{8}{3} \) hours
= (\( \frac{8}{3} \)*60) minutes. => 160 minutes.

Q.50

x can copy 80 pages in 20 hours, x and y together can copy 135 pages in 27 hours. Then y can copy 20 pages in

(1) 20 hours

(2) 3 hours

(3) 24 hours

(4) 12 hours

Ans .

(1) 20 hours

Explanation :
(1) Number of pages copied by x in hour =\( \frac{80}{20} \)=4
Number of pages copied by x and y in 1 hour =\( \frac{135}{27} \)= 5
Number of pages copied by y in 1 hour = 5 – 4 = 1
Required time = 20 hours.

Q.51

A and B can do a piece of work in 15 days. B and C can do a similar work in 12 days and C and A in 10 days. How many days will A take to do the work by himself ?

(1)13

(2)24

(3)40

(4)8

Ans .

(2)24

Explanation :
(2) (A + B)s 1 days work = \( \frac{1}{15} \)....(i)
(B + C)s 1 days work = \( \frac{1}{12} \) .... (ii) and (C + A)s 1 days work = \( \frac{1}{10} \).... (iii)
On adding all three equations, 2 (A + B + C)’s 1 days work = \( \frac{1}{15} \)+\( \frac{1}{12} \)+\( \frac{1}{10} \)
=\( \frac{4+6+5}{60} \) =\( \frac{15}{60} \) = \( \frac{1}{4} \)
(A + B + C)s 1 days work = \( \frac{1}{8} \)....(iv)
By equation (iv) – (ii), A`s 1 days work = \( \frac{1}{8} \)- \( \frac{1}{12} \) = \( \frac{3-2}{24} \) = \( \frac{1}{24} \)
Required time = 24 days.

Q.52

A can do a piece of work in 25 days and B can do the same work in 30 days. They work together for 5 days, how much of work is left ?

(1) \( \frac{11}{30} \)

(2) \( \frac{15}{30} \)

(3)\( \frac{19}{30} \)

(4)\( \frac{12}{30} \)

Ans .

(3)\( \frac{19}{30}\)

Explanation :
(3)(A + B)`s 1 days work =\( \frac{1}{25} \)+\( \frac{1}{30} \) = \( \frac{6+5}{150} \)=\( \frac{11}{150} \)
(A + B)s 5 days work =\( \frac{5*11}{150} \)=\( \frac{11}{30} \)
Remaining work =1-\( \frac{11}{30} \)=\( \frac{30-11}{30} \) =\( \frac{19}{30} \)

Q.53

A and B together can do a piece of work in 6 days. If A can alone do the work in 18 days, then the number of days required for B to finish the work is

(1)10

(2)12

(3)9

(4)15

Ans .

(3) 9

Explanation :
(3)(A + B)s 1 days work = \( \frac{1}{6} \) A`s 1 days work =\( \frac{1}{18} \)
B`s 1 days work =\( \frac{1}{6} \)-\( \frac{1}{18} \)= \( \frac{3-1}{18} \) = \( \frac{2}{18} \) = \( \frac{1}{9} \)
Required time = 9 days

Q.54

A`s 2 days work is equal to B`s 3 days work. If A can complete the work in 8 days then to complete the work B will take

(1)14 days

(2) 12 days

(3) 15 days

(4)16 days

Ans .

(2) 12 days

Explanation :
(2) A`s 2 days work = B`s 3 days work
Time taken by A = 8 days
Time taken by B =\( \frac{8}{2} \) *3 =>12 days.

Q.55

16 men are able to complete a piece of work in 12 days working 14 hours a day. How long will 28 men, working 12 hours a day, take to complete the work ?

(1)10 days

(2)7 days

(3)8 days

(4)10 days

Ans .

(3) 8 days

Explanation :

Q.56

A and B can do a given piece of work in 8 days, B and C can do the same work in 12 days and A, B, C complete it in 6 days. Number of days required to finish the work by A and C is

(1) 16

(2) 8

(3) 12

(4) 24

Ans .

(2) 8 days

Explanation :
(2)(A + B)s 1 days work =\( \frac{1}{8} \)
(B + C)s 1 days work =\( \frac{1}{12} \) and (A + B + C)s 1 days work =\( \frac{1}{6} \) C`s 1 days work = \( \frac{1}{6} \)-\( \frac{1}{8} \)=\( \frac{4-3}{24} \)=\( \frac{1}{24} \)
A`s 1 days work =\( \frac{1}{6} \)-\( \frac{1}{12} \)= \( \frac{2-1}{12} \)= \( \frac{1}{12} \)
(A + C)s 1 days work =\( \frac{1}{12} \)+\( \frac{1}{24} \)=\( \frac{2+1}{24} \)=\( \frac{1}{8} \)
Required time = 8 days

Q.57

. If 90 men can do a certain job in 16 days, working 12 hours per day, then the part of that work which can be completed by 70 men in 24 days, working 8 hours per day is

(1) \( \frac{1}{3} \)

(2) \( \frac{2}{3} \)

(3)\( \frac{7}{9} \)

(4) \( \frac{5}{8} \)

Ans .

(3)\( \frac{7}{9} \)

Explanation :
(3)Using Rule 1,
(M¹D¹T¹) / (W¹) = (M²D²T²) / (W²)
= \( \frac{90*16*12}{1} \) = (70*24*8 ) / (W²)
W² = \( \frac{90*16*12}{70*24*8 }\) = \( \frac{7}{9} \) parts

Q.58

A, B and C can do a work separately in 16, 32 and 48 days respectively. They started the work together but B left off 8 days and C six days before the completion of the work. In what time is the work finished?

(1)10 days

(2) 9 days

(3)12days

(4) 14 days

Ans .

(3)12 days

Explanation :
(3) Let the work be completed in x days.
According to the question,
\( \frac{x}{16} \)+\( \frac{x-8}{32} \)+\( \frac{x-6}{48} \) =1
\( \frac{6x+3x-24+2x-12 }{96} \) =1
11x – 36 = 96
11x = 96 + 36 = 132
x =\( \frac{132}{11} \) =12 days.

Q.59

A and B can do a piece of work in 15 days. B and C can do the same work in 10 days and A and C can do the same in 12 days. Time taken by A, B and C together to do the job is

(1)4 days

(2)9 days

(3)8 days

(4)5 days

Ans .

(3) 8 days

Explanation :
(3) (A+B)s 1 days work =\( \frac{1}{15} \)
(B+C)s 1 days work =\( \frac{1}{10} \) and (A+C)s 1 days work =\( \frac{1}{12} \) On adding all three, 2(A+B+C)s 1 days work =\( \frac{1}{15} \)+\( \frac{1}{10} \)+\( \frac{1}{12} \) =\( \frac{4+6+5}{60} \) =\( \frac{15}{60} \)=\( \frac{1}{4} \)
(A + B + C)s 1 days work =\( \frac{1}{8} \)
Required time = 8 days.

Q.60

A, B and C can complete a work in 10, 12 and 15 days respectively. A left the work 5 days before the work was completed and B left 2 days after A had left. Number of days required to complete the whole work is :

(1) 8\( \frac{2}{3} \)

(2) 6\( \frac{2}{3} \)

(3) 7

(4) 6

Ans .

(3 7

Explanation :
(3) Let the whole work be completed in x days
A`s 1 days work =\( \frac{1}{10} \)
B`s 1 days work =\( \frac{1}{12} \) and C`s 1 days work =\( \frac{1}{15} \)
According to the question, A`s (x – 5) days work + B`s (x – 3) days work + Cs x days work = 1
=>\( \frac{x-5}{10} \) +\( \frac{x-3}{12} \) +\( \frac{x}{15} \) = 1
=> \( \frac{x-5}{10} \)+\( \frac{x-3}{12} \)+\( \frac{x}{15} \) = 1
=> \( \frac{6(x-5)+5(x-3)+4x}{60} \) =1
=> 6x – 30 + 5x – 15 + 4x = 60
=>15x – 45 = 60
=> 15x = 60 + 45 = 105
=> x=\( \frac{105}{15} \) = 7 days.

Q.61

A, B and C can complete a piece of work in 24, 5 an 12 days respectively. Working together, they will complete the same work in :

(1)\( \frac{7}{24} \)days

(2)3\( \frac{1}{13} \)days

(3)4 days

(4) \( \frac{1}{24} \) days

Ans .

(2)3\( \frac{1}{13} \)days

Explanation :
A`s 1 days work =\( \frac{1}{24} \)
B`s 1 days work =\( \frac{1}{5} \) and C 1 days work =\( \frac{1}{12} \)
(A + B + C)s 1 days work = \( \frac{1}{24} \) +\( \frac{1}{5} \) +\( \frac{1}{12} \) =\( \frac{5+24+10}{120} \) =\( \frac{39}{120} \) =\( \frac{13}{40} \)
Required Time=\( \frac{40}{13} \) =3\( \frac{1}{13} \) days.

Q.62

If 20 women can lay a road of length 100m in 10 days. Then 10 women can lay the same road of length 50m in

(1)20 days

(2)15 days

(3)5 days

(4)10 days

Ans .

(4)10 days

Explanation :

Q.63

A can do a piece of work in 9 days while B can do it in 12 days. A and B together can do the work in

(1)5\( \frac{1}{7} \)days

(2)5\( \frac{2}{7} \)days

(3)6\( \frac{1}{7} \)days

(4)6\( \frac{2}{7} \)days

Ans .

(1)5\( \frac{1}{7} \)days

Explanation :
(1) A`s 1 days work =\( \frac{1}{9} \)
B`s 1 days work = 5\( \frac{1}{12} \)
(A + B)s 1 day’s work = \( \frac{1}{9} \)+\( \frac{1}{12} \)= \( \frac{4+3}{36} \) = \( \frac{7}{36} \)
Required time = \( \frac{36}{7} \) =5\( \frac{1}{7} \)days.

Q.64

A man can do a piece of work in 30 hours. If he works with his son then the same piece of work is finished in 20 hours. If the son works alone he can do the work in

(1) 60 hours

(2) 50 hours

(3) 25 hours

(4) 10 hours

Ans .

(1) 60 hours

Explanation :
(1) Let time taken by son be x hours.
Father’s and son`s 1 days work = \( \frac{1}{30} \)+\( \frac{1}{x} \)
\( \frac{1}{30} \)+\( \frac{1}{x} \) =\( \frac{1}{20} \)
=>\( \frac{1}{x} \)= \( \frac{1}{20} \)-\( \frac{1}{30} \)
=\( \frac{3-2}{60} \)=\( \frac{1}{60} \)
=> x = 60 hour.

Q.65

A can do a piece of work in 12 days and B in 20 days. If they together work on it for 5 days, and remaining work is completed by C in 3 days, then in how many days can C do the same work alone?

(1)10 days

(2)9days

(3)12 days

(4)15 days

Ans .

(2)9days

Explanation :
(2) Work done by (A + B) in 5 days = 5(\( \frac{1}{12} \)+\( \frac{1}{20} \) )
=5(\( \frac{5+3}{60} \) ) = \( \frac{40}{60} \) =\( \frac{2}{3} \)
Remaining work = 1-\( \frac{2}{3} \) =\( \frac{1}{3} \)
Time taken by C in doing \( \frac{1}{3} \) work = 3 days
Required time = 3 × 3 = 9 days.

Q.66

A can finish a work in 7 days. B can finish the same work in 9 days. The number days required to finish the same work by both of them together is

(1)1\( \frac{15}{16} \)

(2)2\( \frac{15}{6} \)

(3)3\( \frac{15}{16} \)

(4)4\( \frac{15}{16} \)

Ans .

(3)3\( \frac{15}{16} \)

Explanation :
(3) A`s 1 days work =\( \frac{1}{7} \)
B`s 1 days work =\( \frac{1}{9} \)
(A + B)s 1 days work =\( \frac{1}{7} \)+\( \frac{1}{9} \) =\( \frac{9+7}{63} \) =\( \frac{16}{63} \)
\ Required time =\( \frac{63}{16} \) days =3\( \frac{15}{16} \)days.

Q.67

A and B together can finish a job in 24 days, while A, B and C together can finish the same job in 8 days. C alone will finish the job in

(1) 12 days

(2) 14 days

(3) 16 days

(4) 24 days

Ans .

(1) 12 days

Explanation :
(1) (A + B)s 1 days work =\( \frac{1}{24} \)
(A + B + C)s 1 days work =\( \frac{1}{8} \)
C`s 1 days work = \( \frac{1}{24} \) -\( \frac{1}{8} \) =\( \frac{3-1}{24} \) =\( \frac{2}{24} \) =\( \frac{1}{12} \)
Required time = 12 days.

Q.68

A can do a piece of work in 12 days and B in 24 days. If they work together, in how many days will they finish the work?

(1)12days

(2)20days

(3)15 days

(4) 8 days

Ans .

(4) 8 days

Explanation :
(4) (A + B)’s 1 day’s work=\( \frac{1}{12} \)+\( \frac{1}{24} \)=\( \frac{2+1}{24} \)=\( \frac{3}{24} \)=\( \frac{1}{8} \)
Required time = 8 days.

Q.69

A, B and C working separately can do a piece of work in 11 days, 20 days and 55 days respectively. In how many days, the work will be completed if A is assisted by B and C on alternate days ?

(1)2

(2)6

(3)4

(4)8

Ans .

(4)8

Explanation :
(4) (A + B)s 1 days work =\( \frac{1}{11} \)+\( \frac{1}{20} \) =\( \frac{20+11}{220} \)=\( \frac{31}{220} \)
(A + C)’s 1 days work =\( \frac{1}{11} \)+\( \frac{1}{55} \)=\( \frac{5+1}{55} \)=\( \frac{6}{55} \)
Work done in first two days = \( \frac{31}{220} \)+\( \frac{6}{55} \) =\( \frac{31+24}{220} \)=\( \frac{55}{220} \)=\( \frac{1}{4} \)
Required time = 2 × 4 = 8 days.

Q.70

A and B together can do a piece of work in 6 days and A alone can do it in 9 days. The number of days B will take to do it alone is

(1)18 days

(2)24 days

(3)9 days

(4)12 days

Ans .

(1)18 days

Explanation :
(1) (A + B)s 1 days work =\( \frac{1}{6} \)
A`s 1 days work =\( \frac{1}{9} \)
B’s 1 day’s work =\( \frac{1}{6} \)-\( \frac{1}{9} \)=\( \frac{3-2}{18} \)=\( \frac{1}{18} \)
Required time = 18 days.

Q.71

A can do a piece of work in 18 days. He worked at it for 12 days and B finished the remaining work in 8 days. B alone can do the whole work in

(1) 16 days

(2) 24 days

(3) 28 days

(4) 29 days

Ans .

(2) 24 days

Explanation :
A`s 1 days work =\( \frac{1}{18} \)
A`s 12 days work =\( \frac{12}{18} \)=\( \frac{2}{3} \)
=>Remaining work =1-\( \frac{2}{3} \) =\( \frac{1}{3} \)
Time taken by B in doing \( \frac{1}{3} \) work = 8 days
Time taken by B in doing whole work = 3 × 8 = 24 days .

Q.72

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

(1)4 days

(2)6 days

(3)8 days

(4)12 days

Ans .

(3)8 days

Explanation :
(3) (A + B)s 1 days work=\( \frac{1}{8} \) ... (i)
(B + C)s 1 days work= \( \frac{1}{12} \).... (ii) and (A + B + C)s 1 days work =\( \frac{1}{6} \)... (iii)
By equations (i) + (ii) – (iii), Bs 1 days work =\( \frac{1}{8} \)+\( \frac{1}{12} \)-\( \frac{1}{6} \) = \( \frac{3+2-4}{24} \) = \( \frac{1}{24} \) .... (iv)
By equations (iii) – (iv), (A + C)’s 1 days work =\( \frac{1}{6} \)-\( \frac{1}{24} \) = \( \frac{4-1}{24} \)= \( \frac{3}{24} \) =\( \frac{1}{8} \)
Required time = 8 days

Q.73

A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, the time A alone will take to finish the work is

(1)4 days

(2)6 days

(3)8 days

(4)12 days

Ans .

(4)12 days

Explanation :
(4) Let time taken by A be x days.
Time taken by B = 3x days According to the question,
\( \frac{1}{x} \)+\( \frac{1}{3x} \)=\( \frac{1}{9} \)
=>\( \frac{3+1}{3x} \) =\( \frac{1}{9} \)
=>3x = 4 × 9
=> x = \( \frac{4*9}{3} \) =12 days.

Q.74

If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?

(1) 4 days

(2) 3 days

(3) 40 days

(4) 100 days

Ans .

(4) 100 days

Explanation :

Q.75

X can do a piece of work in 'p' days and Y can do the same work in 'q' days. Then the number of days in which X and Y can together do that work is

(1)(\( \frac{p+q}{2} \)

(2)(\( \frac{1}{p} \)+(\( \frac{1}{q} \)

(3)(\( \frac{pq}{p+q} \)

(4)pq

Ans .

(3)(\( \frac{pq}{p+q} \)

Explanation :
(3) X`s 1 days work =\( \frac{1}{p} \)
Y`s 1 day’s work =\( \frac{1}{q} \)
(X + Y)s 1 days work= \( \frac{1}{p} \)+\( \frac{1}{q} \)=\( \frac{q+p}{pq} \)
Required time =(\( \frac{pq}{p+q} \).

Q.76

A can do a piece of work in 8 days and B can do it in 10 days separately. How many days would it take for both A and B to finish the same work together ?

(1)\( \frac{33}{8} \)

(2)\( \frac{40}{9} \)

(3)\( \frac{41}{10} \)

(4)\( \frac{42}{11} \)

Ans .

(2)\( \frac{40}{9} \)

Explanation :
(2) A`s 1 days work =\( \frac{1}{8} \) B`s 1 days work =\( \frac{1}{10} \)
(A + B)s 1 days work = \( \frac{1}{8} \)+\( \frac{1}{10} \) =\( \frac{5+4}{40} \)=\( \frac{9}{40} \)
Required time = \( \frac{40}{9} \) days

Q.77

A and B together can do a piece of work in 36 days, B and C together can do it in 24 days. A and C together can do it in 18 days. The three working together can finish the work in

(1) 8 days

(2) 16 days

(3) 30 days

(4) 32days

Ans .

(2) 16 days

Explanation :
(2) (A + B)s 1 days work =\( \frac{1}{36} \)
(B + C)s 1 days work = \( \frac{1}{24} \) and (A + C)s 1 days work =\( \frac{1}{18} \)
On adding all three, 2 (A + B + C)s 1 days work =\( \frac{1}{36} \)+\( \frac{1}{24} \)+\( \frac{1}{18} \) = \( \frac{2+3+4}{72} \) =\( \frac{9}{72} \) =\( \frac{1} {8} \)
(A + B + C)’s 1 day’s work =\( \frac{1}{36} \)
Required time = 16 days .

Q.78

Koushik can do a piece of work in x days and Krishnu can do the same work in y days. If they work together, then they can do the work in

(1)(x + y) days

(2)\( \frac{1}{x+y} \)days

(3)\( \frac{xy}{x+y} \) days

(4) \( \frac{x+y}{xy} \) days

Ans .

\( \frac{xy}{x+y} \) days

Explanation :
(3) Koushik`s 1 days work =\( \frac{1}{x} \)
Krishnu`s 1 days work =\( \frac{1}{y} \)
One days work of both =\( \frac{1}{x} \)+\( \frac{1}{y} \) =\(\frac{x+y}{xy} \)
Required time =\( \frac{xy}{x+y} \) days.

Q.79

A canal of a village can be cleanedby 24 villagers in 12 days. The number of days in which 36 villagers can clean the canal is

(1)18

(2)8

(3)72

(4)16

Ans .

(2)8

Explanation :
M₁D₁ = M₂D₂
=>24 × 12 = 36 × D₂
= D₂ =\( \frac{24*12}{36} \) = 8 days.

Q.80

A and B can do a piece of work in 18 days, B and C in 24 days, A and C in 36 days. Working together they can do the work in

(1)12 days

(2)13 days

(3)16 days

(4)26 days

Ans .

(1)18 days

Explanation :
(3) (A + B)s 1 days work =\( \frac{1}{18} \)
(B + C)s 1 days work =\( \frac{1}{24} \) and (C + A)s 1 days work =\( \frac{1}{36} \)
On adding all three, 2 (A + B + C)s 1 day’s work =\( \frac{1}{18} \)+\( \frac{1}{24} \)+\( \frac{1}{36} \)=\( \frac{4+3+2}{72} \)=\( \frac{9}{72} \)=\( \frac{1}{8} \)
(A + B + C)’s 1 days work =\( \frac{1}{16} \)
Required time = 16 days .

Q.81

A can do as much work in 4 days as B can do in 5 days, and B can do as much work in 6 days as C in 7 days. In what time will C do a piece of work which A can do in a week ?

(1) 10\( \frac{5}{24} \) days

(2)4\( \frac{4}{5} \) days

(3) 6\( \frac{8}{15} \) days

(4) 12\( \frac{6}{19} \) days

Ans .

(1) 10\( \frac{5}{24} \) days

Explanation :
(1) A`s 4 days work = Bs 5 days work
=> A : B = 4 : 5
Again, B : C = 6 : 7
=> A : B : C = 4 × 6 : 5 × 6 : 5 × 7 = 24 : 30 : 35
Q Time taken by A = 7 days
Time taken by C =\( \frac{35}{24} \) * 7 =\( \frac{245}{24} \) =10\( \frac{5}{24} \) days.

Q.82

If 42 persons consume 144 kg of wheat in 15 days, then in how many days will 30 persons consume 45 kg of wheat ?

(1)8 days

(2)7 days

(3)12 days

(4)6 days

Ans .

(2)7 days

Explanation :

Q.83

A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours, the number of hours taken by the father, to do the job alone is

(1)1

(2)2

(3)3

(4)4

Ans .

(2)2

Explanation :
(2) Work done by two sons in an hour =\( \frac{1}{3} \)+\( \frac{1}{6} \)=\( \frac{2+1}{6} \)=\( \frac{1}{2} \)
Work done by father in an hour =\( \frac{1}{2} \)
Required time = 2 hours

Q.84

A can do a piece of work in 10 days, B can do it in 12 days and C can do it in 15 days. In how many days will A, B and C finish it, working all together?

(1) 6 days

(2) 5\( \frac{1}{4} \) days

(3) 4\( \frac{4}{11} \) days

(4)4 days

Ans .

(4) 4 days

Explanation :
A`s 1 days work =\( \frac{1}{10} \)
B`s 1 days work =\( \frac{1}{12} \) and C`s 1 day’s work =\( \frac{1}{15} \)
(A + B + C)’s 1 days work = \( \frac{1}{10} \) +\( \frac{1}{12} \) +\( \frac{1}{15} \) =\( \frac{6+5+4}{60} \) =\( \frac{15}{60} \) =\( \frac{1}{4} \)
Required time = 4 days.

Q.85

If 5 persons together can make 5 mats in 5 hours, then 10 persons in 10 hours will make

(1) 20 mats

(2) 10 mats

(3) 15 mats

(4) 5 mats

Ans .

(1) 20 mats

Explanation :

=>5 × 5 × x = 10 × 10 × 5 => x =\( \frac{10*10*5}{5*5} \) = 20 mats.

Q.86

A and B together can do a piece of work in 12 days while A alone can do the same work in 30 days. B alone can do it in

(1)18 days

(2)20 days

(3)15 days

(4)22 days

Ans .

(2)20 days

Explanation :
(2) (A + B)s 1 days work =\( \frac{1}{12} \)
As 1 days work =\( \frac{1}{30} \)
B`s 1 day’s work =\( \frac{1}{12} \)-\( \frac{1}{30} \) =\( \frac{5-2}{60} \) =\( \frac{1}{20} \) Required time = 20 days

Q.87

Ganesh, Ram and Sohan together can complete a work in 16days. If Ganesh and Ram together can complete the same work in 24 days, the number of days Sohan alone takes, to finish the work is

(1)40

(2)48

(3)32

(4)30

Ans .

(2)48

Explanation :
(2) (Ganesh + Ram + Sohan)s 1 days work =\( \frac{1}{16} \)
(Ganesh + Ram)s 1 days work = \( \frac{1}{24} \)
Sohan`s 1 days work = \( \frac{1}{16} \) -\( \frac{1}{24} \) =\( \frac{3-2}{48} \) =\( \frac{1}{48} \)
Required time = 48 days.

Q.88

A and B can do a piece of work in 72 days. B and C can do it in 120 days and A and C can do it in 90 days. A alone can do it in :

(1) 120 days

(2)130days

(3) 150 days

(4) 100 days

Ans .

(1) 120 days

Explanation :
(1) (A + B)s 1 days work= \( \frac{1}{72} \) ..... (i)
(B + C)s 1 days work = \( \frac{1}{120} \).... (ii) and (C + A)’s 1 day’s work = \( \frac{1}{90} \)..... (iii)
On adding all three, 2 (A + B + C)s 1 days work =\( \frac{1}{72} \)+\( \frac{1}{120} \)+\( \frac{1}{90} \)
=\( \frac{5+3+4}{360} \) =\( \frac{12}{360} \)=\( \frac{1}{30} \)
(A + B + C)s 1 days work= \( \frac{1}{60} \)..... (iv)
A`s 1 days work = Equation (iv) – (ii),
\( \frac{1}{60} \)-\( \frac{1}{120} \)=\( \frac{2-1}{120} \)=\( \frac{1}{120} \)
Required time = 120 days .

Q.89

If 35 men can finish a piece of work in 8 days, then the number of men who can do the same work in 10 days is :

(1)38

(2)28

(3)19

(4)17

Ans .

(2)28

Explanation :

Q.90

A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?

(1)42\( \frac{3}{4} \) days

(2)27\( \frac{1}{7} \) days

(3)17\( \frac{1}{7} \) days

(4)70 days

Ans .

(3)17\( \frac{1}{7} \) days

Explanation :
(3) A`s 1 days work =\( \frac{1}{30} \)
B`s 1 days work =\( \frac{1}{40} \)
(A + B)’s 1 day’s work =\( \frac{1}{30} \)+\( \frac{1}{40} \)= \( \frac{4+3}{120} \)=\( \frac{7}{120} \)
Required time =\( \frac{120}{7} \)=17\( \frac{1}{7} \).

TYPE-II

Q.1

A and B can do a work in 18 and 24 days respectively. They worked together for 8 days and then A left. The remaining work was finished by B in

(1) 5 days

(2) 5\( \frac{1}{3} \)days

(3) 8 days

(4) 10 days

Ans .

(2) 5\( \frac{1}{3} \)days

Explanation :
(2) A can finish the work in 18 days.
A`s one days work = \( \frac{1}{18} \)
Similarly, B`s one days work = \( \frac{1}{24} \)
(A + B)s 8 days work =( \( \frac{1}{18} \)+\( \frac{1}{24} \)) *8 =\( \frac{7}{72} \) *8=\( \frac{7}{9} \)
Remaining work = 1-\( \frac{7}{9} \)=\( \frac{2}{9} \)
Time taken to finish the remaining work by B is \( \frac{2}{9} \) *24 = \( \frac{16}{3} \) =5\( \frac{1}{3} \)days.

Q.2

A can do a piece of work in 12 days and B can do it in 18 days. They work together for 2 days and then A leaves. How long will B take to finish the remaining work ?

(1) 6 days

(2) 8 days

(3) 10 days

(4) 13 days

Ans .

(4) 13 days

Explanation :
(4) (A+B)s 2 days work =2(\( \frac{1}{12} \) +\( \frac{1}{18} \) ) =\( \frac{10}{36} \)
Remaining work = 1 - \( \frac{10}{36} \) =\( \frac{26} {36} \)
Time taken by B to complete \( \frac{26}{36} \) part of work
=>\( \frac{26}{36} \) *18= 13 days.

Q.3

A and B can do a job in 6 and 12 days respectively. They began the work together but A leaves after 3 days. Then the total number of days needed for the completion of the work is :

(1) 4 days

(2) 5 days

(3) 6 days

(4)9 days

Ans .

(3) 6 days

Explanation :
(3) A1s one days work = \( \frac{1}{6} \)
B`s one days work =\( \frac{1}{12} \)
(A + B)s one days work =\( \frac{1}{6} \) +\( \frac{1}{12} \) =\( \frac{2+1}{12} \) =\( \frac{1}{4} \)
(A + B)s three days work =\( \frac{3}{4} \)
Remaining work = 1-\( \frac{3}{4} \)= \( \frac{1}{4} \)
Total required number of days = \( \frac{1}{4} \)*\( \frac{12}{1} \) +3= 3 + 3 = 6 days.

Q.4

A and B can do a piece of work in 30 days while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work ?

(1) 18 days

(2)24 days

(3) 30 days

(4) 36 days

Ans .

(1) 18 days

Explanation :
(1) (A + B)s days work =\( \frac{1}{30} \)
(B + C)s 1 days work =\( \frac{1}{24} \) and (C + A)s 1 days work =\( \frac{1}{20} \)
2 (A + B + C)s 1 days work =\( \frac{1}{30} \)+\( \frac{1}{24} \)+\( \frac{1}{20} \) =\( \frac{4+5+6}{120} \)=\( \frac{15}{120} \)=\( \frac{1}{8} \)
(A + B + C)s 1 days work =\( \frac{1}{16} \)
(A + B + C)s 10 days’ work =\( \frac{10}{16} \)=\( \frac{5}{8} \)
Remaining work = 1 -\( \frac{5}{8} \) =\( \frac{3}{8} \)
This part of work is done by A alone.
Now A`s 1 day’s work =\( \frac{1}{16} \) -\( \frac{1}{24} \) =\( \frac{3-2}{48} \) =\( \frac{1}{48} \)
The required no. of days =\( \frac{3}{8} \)* 3= 18 days.

Q.5

A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finishedthe remaining work. In how many days A alone can finish the job ?

(1) 50 days

(2) 60 days

(3) 48 days

(4) 54 days

Ans .

(2)60 days

Explanation :
2) (A+B)s 1 days work =\( \frac{1}{30} \)
(A + B)s 20 days work =\( \frac{20}{30} \) =\( \frac{2}{3} \)
Remaining work =1-\( \frac{2}{3} \)=\( \frac{1}{3} \)
Now,\( \frac{1}{3} \)part of work is done by A in 20 days.
Whole work will be done by A alone in 20 × 3 = 60 days

Q.6

8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed?

(1) 2

(2) 3

(3) 4

(4) 5

Ans .

(3) 4

Explanation :

Q.7

A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in :

(1) 5 days

(2) 6 days

(3) 10 days

(4) 10\( \frac{1}{2} \) days

Ans .

(3) 10 days

Explanation :
(3) Work done by (B + C) in 3 days = 3* (\( \frac{1}{9} \) +\( \frac{1}{12} \))
= \( \frac{1}{3} \)+\( \frac{1}{4} \)=\( \frac{4+3}{12} \)=\( \frac{7}{12} \)
Remaining work = 1-\( \frac{7}{12} \) =\( \frac{5}{12} \)
This part of work is done by A alone.
Now, \( \frac{1}{24} \) part of work is done by A in 1 day.
=> \( \frac{5}{12} \) part of work will be done by A in = 24 ´*\( \frac{5}{12} \) = 10 days.

Q.8

A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished in 11 days less. How many persons were originally there ?

(1)17

(2) 24

(3) 30

(4) 22

Ans .

(2) 24 days

Explanation :
(2) Originally, let there be x men Now, more men, less days (x + 6) : x : : 55 : 44
so,\( \frac{x+6}{x} \)=\( \frac{55}{44} \) =\( \frac{5}{4} \)
or 5x = 4x + 24 or x = 24.

Q.9

A and B working separately can do a piece of work in 10 days and 15 days respectively. If they work on alternate days beginning with A, in how many days will the work be completed ?

(1) 18 days

(2) 13 days

(3) 12 days

(4) 6 days

Ans .

(3) 12 days

Explanation :
(3) Work done by 2 (A + B) in one day =( \frac{1}{10} \)+( \frac{1}{15} \) =( \frac{3+2}{30} \)=( \frac{5}{30} \)=( \frac{1}{6} \)
Work done by (A + B) in oneday =( \frac{1}{12} \)
(A + B) can complete the work in 12 days

Q.10

A and B can do a piece of work in 28 and 35 days respectively.They began to work together but A leaves after sometime and B completed remaining work in 17 days. After how many days did A leave ?

(1)14\( \frac{2}{5} \)days

(2)9 days

(3)8 days

(4)7 \( \frac{5}{9} \) days

Ans .

(3)8 days

Explanation :
(3) Let A worked for x days.
According to question \( \frac{x}{28} \)+\( \frac{(x+17)}{35} \) =1
=>\( \frac{5x+4(x+17)}{140} \) =1
=>5x + 4x + 68 = 140
=>9x = 140 – 68 = 72
=> x = 8
A worked for 8 days

Q.11

A and B can complete a work in 15 days and 10 days respectively.They started doing the work together but after 2 days,B had to leave and A alone completed the remaining work. The whole work was completed in :

(1)10 days

(2)8 days

(3)12 days

(4)15 days

Ans .

(3)12 days

Explanation :
(3) Work done by (A + B) in 1 day =\( \frac{1}{15} \)+\( \frac{1}{10} \)=\( \frac{2+3}{30} \)=\( \frac{1}{6} \)
(A + B)s 2 days work =\( \frac{2}{6} \) =\( \frac{1}{3} \)
Remaining work =1 -\( \frac{1}{3} \) =\( \frac{2}{3} \)
This part is done by A alone.
one work is done by A in 15 days.
\( \frac{2}{3} \) work is done in 15*\( \frac{2}{3} \)
= 10 days.
Total number of days = 10 + 2 = 12 days

Q.12

A and B can do a piece of work in 20 days and 12 days respectively.A started the work alone and then after 4 days B joined him till the completion of the work. How long did the work last ?

(1)10 days

(2)20 days

(3)15 days

(4)6 days

Ans .

(4)10 days

Explanation :
(1) A`s 1 day`s work =\( \frac{1}{20} \).
A`s 4 days work =\( \frac{4}{20} \) =\( \frac{1}{5} \)
This part is completed by A and B together.
Now, (A + B)s 1 days work = \( \frac{1}{20} \)+\( \frac{1}{12} \)=\( \frac{3+5}{60} \)=\( \frac{8}{60} \)=\( \frac{2}{15} \)
Now,\( \frac{2}{15} \)work is done by (A +B) in 1 day.
\( \frac{4}{5} \) work is done in .
=\( \frac{15}{2} \)*\( \frac{4}{5} \) = 6 days
Hence, the work lasted for 4 + 6 = 10 days.

Q.13

A and B can do a work in 45 days and 40 days respectively. They began the work together but A left after some time and B completed the remaining work in 23 days. After how many days of the start of the work did A leave ?

(1)10 days

(2)9 days

(3)8 days

(4)5 days

Ans .

(2)9 days

Explanation :
(2) (A + B)s 1 days work =(\( \frac{1}{45} \) +\( \frac{1}{40} \) ) =\( \frac{8+9}{360} \) =\( \frac{17}{360} \)
Work done by B in 23 days = \( \frac{1}{4} \) * 23 =\( \frac{23}{40} \)
Remaining work = 1- \( \frac{23}{40} \)= \( \frac{17}{40} \)
Now,\( \frac{17}{40} \)work was done by (A + B) in 1 day
\( \frac{17}{40} \) work was done by (A + B) in 1 * \( \frac{360}{17} \) *\( \frac{17}{40} \) = 9 days.
Hence, A left after 9 days.

Q.14

A man and a boy can complete a work together in 24 days. If for the last six days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone ?

(1)72 days

(2)20 days

(3)24 days

(4)36 days

Ans .

(1)72 days

Explanation :

Q.15

A and B together can complete a work in 8 days. B alone can complete that work in 12 days. B alone worked for four days. After that how long will A alone take to complete the work ?

(1)15 days

(2)18 days

(3)16 days

(4)20 days

Ans .

(3)16 days

Explanation :
(3) Time taken by A = \( \frac{8*12}{4} \) = 24days.
Work done of by B = \( \frac{4}{12} \)=\( \frac{1}{3} \)
Remaining work =1-\( \frac{1}{3} \) = \( \frac{2}{3} \)
A can complete a work in 24 days
A can complete \( \frac{2}{3} \) part of work in 24* \( \frac{2}{3} \) = 16 days.

Q.16

A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in

(1)14\( \frac{1}{3} \) days

(2)15\( \frac{2}{3} \) days

(3)16\( \frac{1}{3} \) days

(4)18\( \frac{2}{3} \) days

Ans .

(1)14\( \frac{1}{3} \) days

Explanation :
(1) A`s 1 days work = \( \frac{1}{12} \)
B`s 1 days work = \( \frac{1}{18} \)
Part of work done by A and B in first two days = \( \frac{1}{12} \)+ \( \frac{1}{18} \)= \( \frac{3+2}{36} \)= \( \frac{5}{36} \)
Part of work done by A and B in 14 days =\( \frac{35}{36} \)
[14 days to be taken randomly] Remaining work = 1-\( \frac{35}{36} \) =\( \frac{1}{36} \)
Now A will work for 15th day. A will do the \( \frac{1}{36} \) work in \( \frac{1}{36} \)*12 =\( \frac{1}{3} \) day.
Total Work will be done in 14\( \frac{1}{3} \) days.

Q.17

A, B and C can complete a work in 10, 12 and 15 days respectively. They started the work together. But A left the work before 5 days of its completion. B also left the work 2 days after A left. In how many days was the work completed?

(1)4 days

(2)5 days

(3)7 days

(4)8 days

Ans .

(3)7 days

Explanation :
(3) Let the work be completed in x days.
According to the question ,\( \frac{x-5}{10} \)+\( \frac{x-3}{12} \)+\( \frac{x}{15} \)=1
=>\( \frac{6x-30+5x-15+4x}{60} \) =1
=>15x – 45 = 60 ,/br> => 15x = 105
=> x =\( \frac{105}{15} \) = 7 days.

Q.18

A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C worked together for two days and then A was replaced by B. In how many days, altogether, was the work completed ?

(1)12 days

(2)10 days

(3)6 days

(4)8 days

Ans .

(4)8 days

Explanation :

Q.19

40 men can complete a work in 40 days. They started the work together. But at the end of each 10th day, 5 men left the job. The work would have been completed in

(1)56\( \frac{2}{3} \) days

(2)53\( \frac{1}{3} \) days

(3)52 days

(4)53 days

Ans .

(1)56\( \frac{2}{3} \) days

Explanation :

Q.20

A can do a piece of work in 18 days and B in 12 days. They began the work together, but B left the work 3 days before its completion. In how many days, in all, was the work completed?

(1)12 days

(2)10 days

(3)9.6 days

(4)9 days

Ans .

(4)9 days

Explanation :
(4) Let the work be finished in x days.
According to the question,
A worked for x days while B worked for (x – 3) days
\( \frac{x}{18} \)+\( \frac{x-3}{12} \)=1
=>\( \frac{2x+3x-9}{36} \) = 1
=> 5x – 9 = 36
=> 5x = 45
=> x = \( \frac{45}{5} \)= 9
Hence, the work was completed in 9 days.

Q.21

A and B can separately completea piece of work in 20 days and 30 days respectively. They worked together for some time,then B left the work. If A completed the rest of the work in 10 days, then B worked for

(1)6 days

(2)8 days

(3)12 days

(4)16 days

Ans .

(1)6 days

Explanation :
(1) Let A and B worked together for x days
According to the question,
Part of work done by A for (x + 10) days + part of work done by B for x days = 1
=> \( \frac{x+10}{20} \) +\( \frac{x}{30} \) = 1
=> \( \frac{3x+30+2x}{60} \) = 1
=>5x + 30 = 60
=> 5x = 30
=> x= \( \frac{30}{5} \) = 6 days.

Q.22

A and B alone can complete workin 9 days and 18 days respectively. They worked together; however 3 days before the completion of the work A left. In how many days was the work completed ?

(1)13 days

(2)8 days

(3)6 days

(4)5 days

Ans .

(2)8 days

Explanation :
(2) Let the work be completed in x days.
According to the question,
A worked for (x –3) days, while B worked for x days.
\( \frac{x-3}{9} \) +\( \frac{x}{18} \) = 1
=>\( \frac{2x-6+x}{18} \) = 1 => 3x–6 = 18
=>3x = 18 + 6 = 24
=> x =\( \frac{24}{3} \) = 8 days.

Q.23

A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is

(1))10 days

(2)12 days

(3)15 days

(4)16 days

Ans .

(3)15 days

Explanation :
(3) (B + C)s 2 days work= 2(\( \frac{1}{30} \) + (\( \frac{1}{20} \))
= 2(\( \frac{2+3}{60} \)) = \( \frac{1}{6} \) part
Remaining work = 1- \( \frac{1}{6} \)= \( \frac{5}{6} \) part.
Time taken by A to complete this part of work \( \frac{5}{6} \) *18 = 15 days.

Q.24

A alone can complete a work in 18 days and B alone in 15 days. B alone worked at it for 10 days and then left the work. In how many more days, will A alone complete the remaining work ?

(1)5 days

(2)5\( \frac{1}{2} \) days

(3)6 days

(4)8 days

Ans .

(3)6 days

Explanation :
(3) Part of work done by B in 10 days = 10*\( \frac{1}{15} \) = \( \frac{2}{3} \)
Remaining work =1 - \( \frac{1}{2} \) = \( \frac{1}{3} \)
Time taken by A = \( \frac{1}{3} \)*18 = 6 days.

Q.25

A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately with A beginning, the work would be completed in

(1)10\( \frac{2}{3} \)days

(2)10\( \frac{1}{2} \)days

(3)10\( \frac{1}{4} \)days

(4)10\( \frac{1}{3} \)days

Ans .

(3)10\( \frac{1}{4} \)days

Explanation :
(3) Part of work done by A and B in first two days \( \frac{1}{9} \) +\( \frac{1}{12} \) = \( \frac{4+3}{36} \) = \( \frac{7}{36} \)
Part of work done in first 10 days = \( \frac{35}{36} \)
Remaining work= 1-\( \frac{35}{36} \) = \( \frac{1}{36} \)
Now it is the turn of A.
Time taken by A =\( \frac{1}{36} \)*9 = \( \frac{1}{4} \)day
Total time = 10 +\( \frac{1}{4} \) =10\( \frac{1}{4} \)days.

Q.26

A and B together can complete a work in 12 days. A alone can complete in 20 days. If B does the work only half a day daily, then in how many days A and B together will complete the work ?

(1)10 days

(2)20 days

(3)11 days

(4)15 days

Ans .

(4)15 days

Explanation :
(4) B`s 1 days work =\( \frac{1}{12} \)-\( \frac{1}{20} \)= \( \frac{5-3}{60} \) =\( \frac{1}{30} \)
B`s \( \frac{1}{2} \)days work = \( \frac{1}{60} \)
(A + B)s 1 days work = \( \frac{1}{20} \) + \( \frac{1}{60} \) = \( \frac{3+1}{60} \)= \( \frac{1}{15} \)
[ B works for half day daily]
Hence, the work will be completed in 15 days

Q.27

A and B can do a piece of work in 12 days and 15 days respectively. They began to work together but A left after 4 days. In how many more days would B alone complete the remaining work ?

(1)\( \frac{20}{3} \) days

(2)\( \frac{25}{3} \) days

(3)6 days

(4)5 days

Ans .

(3)6 days

Explanation :
. (3) Part of the work done by A and B in 4 days = 2*(\( \frac{1}{12} \)+\( \frac{1}{15} \)) = 4\( \frac{5+4}{60} \)
= 4*\( \frac{9}{60} \) =\( \frac{3}{5} \)
Remaining work = 1-\( \frac{3}{5} \) =\( \frac{2}{5} \)
Time taken by B to complete the remaining work =\( \frac{2}{5} \) *15 =6 days

Q.28

X alone can complete a piece of work in 40 days. He worked for 8 days and left. Y alone completed the remaining work in 16 days. How long would X and Y together take to complete the work ?

(1)13\( \frac{1}{3} \) days

(2)14 days

(3)15 days

(4)16 \( \frac{2}{3} \) days

Ans .

(1)13\( \frac{1}{3} \) days

Explanation :
(1) Part of the work done by X in 8 days=\( \frac{8}{40} \)=\( \frac{1}{5} \)
Remaining work = 1-\( \frac{1}{5} \)=\( \frac{4}{5} \)
This part of work is done by Y in 16 days.
Time taken by Y in doing 1 work =\( \frac{16*5}{4} \) = 20 days.
Work done by X and Y in 1 day = \( \frac{1}{40} \)+\( \frac{1}{20} \)=\( \frac{1+2}{40} \)=\( \frac{3}{40} \)
Hence, both together will complete the work in\( \frac{40}{3} \) i.e13\( \frac{1}{3} \) days

Q.29

A, B and C can do a piece of work in 30, 20 and 10 days respectively. A is assisted by B on one day and by C on the next day, alternately. How long would the work take to finish ?

(1)9\( \frac{3}{8} \) days

(2)4\( \frac{8}{8} \) days

(3)8\( \frac{4}{13} \) days

(4)3\( \frac{9}{13} \) days

Ans .

(1)9\( \frac{3}{8} \) days

Explanation :
(1) Work done in first two days =\( \frac{2}{30} \)+\( \frac{1}{10} \)+\( \frac{1}{20} \)=\( \frac{1}{15} \)+\( \frac{1}{20} \)+\( \frac{1}{10} \)
=\( \frac{4+3+6}{60} \) = \( \frac{13}{60} \)
Work done in first 8 days =\( \frac{52}{60} \) Remaining work = 1-\( \frac{52}{60} \) = \( \frac{8}{60} \) = \( \frac{2}{15} \)
(A + B)s 1 days work = \( \frac{1}{30} \) +\( \frac{1}{20} \)=\( \frac{2+3}{60} \)=\( \frac{1}{12} \)
Remaining work =\( \frac{2}{15} \) -\( \frac{1}{12} \) =\( \frac{8-5}{60} \)=\( \frac{3}{60} \)=\( \frac{1}{20} \)
(A + C)s 1 days work =\( \frac{1}{30} \)+\( \frac{1}{10} \)=\( \frac{1+3}{30} \)=\( \frac{2}{15} \)
Time taken =\( \frac{1}{20} \)*\( \frac{15}{2} \)
=\( \frac{3}{8} \) day.
Total time = 9 +\( \frac{3}{8} \) =9\( \frac{3}{8} \) days

Q.30

A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in

(1)5 days

(2)7 days

(3)11 days

(4)3 days

Ans .

(1)5 days

Explanation :
(1) Work done by B in 9 days = \( \frac{9}{12} \) =\( \frac{3}{4} \)part
Remaining work = 1- \( \frac{3}{4} \)= \( \frac{1}{4} \)which is done by A
Time taken by A =\( \frac{1}{4} \)*20 = 5days.

Q.31

A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 of which B has been destroying; how many days must A now work alone to complete the work ?

(1) 7 days

(2) 7\( \frac{1}{3} \) days

(3) 7\( \frac{2}{3} \) days

(4) 8 days

Ans .

(2) 7\( \frac{1}{3} \) days

Explanation :
(2) Work done by A in 6 days =\( \frac{6}{8} \)=\( \frac{3}{4} \)part
Work destroyed by B in 2 days =\( \frac{2}{3} \)part
Remaining work after destruction = \( \frac{3}{4} \)- \( \frac{2}{3} \)= \( \frac{9-8}{12} \)=\( \frac{1}{12} \)
Now, time taken by A in doing \( \frac{11}{12} \) part
\( \frac{11}{12} \) * 8 = \( \frac{22}{3} \) =7\( \frac{1}{3} \)days.

Q.32

A can finish a work in 18 days and B can do the same work in 5 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

(1)6 days

(2)5 \( \frac{1}{2} \) days

(3)5 days

(4)8 days

Ans .

(1)6 days

Explanation :
(1) Work done by B in 10 days =\( \frac{10}{15} \)=\( \frac{2}{3} \)
Remaining work = 1-\( \frac{2}{3} \)=\( \frac{1}{3} \)
Time taken by A to complete the work = \( \frac{1}{3} \) *18 = 6 days.

Q.33

A and B together can do a piece of work in 12 days which B and C together can do in 16 days.After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days B could finish the work ?

(1)48 days

(2)24 days

(3)16 days

(4)12 days

Ans .

(1)48 days

Explanation :

Q.34

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day ?

(1) 10 days

(2) 12 days

(3) 15 days

(4) 20 days

Ans .

(3) 120 days

Explanation :
(3) (A + B + C)s 1 days work = \( \frac{1}{20} \)+\( \frac{1}{30} \)+\( \frac{1}{60} \) = \( \frac{3+2+1}{60} \) = \( \frac{1}{10} \)
A`s 2 days work =\( \frac{2}{20} \)=\( \frac{1}{10} \)
Work done in first three days= \( \frac{1}{10} \)+\( \frac{1}{10} \)=\( \frac{2}{10} \)=\( \frac{1}{5} \)
[A`s work for 2 days + (A + B + C) work on 3rd day]
Hence, the work will be finished in 15 days.

Q.35

A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in

(1)10 days

(2)4 days

(3)6 days

(4)8 days

Ans .

(3)6 days

Explanation :
(3) (A + B)`s 2 days work =\( \frac{2}{3} \)
Remaining Work =1 - \( \frac{2}{3} \) = \( \frac{1}{3} \)
Time taken by A in destroying \( \frac{1}{3} \)work = 2 days
Time taken by A in completing the work = 6 days
B`s 1 days work = \( \frac{1}{3} \)-\( \frac{1}{6} \) =\( \frac{2-1}{6} \) =\( \frac{1}{6} \)
B alone will complete the work in 6 days.

Q.36

A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work ?

(1)25 days

(2)30 days

(3)24 days

(4)20 days

Ans .

(3)24 days

Explanation :
(3) Work done by A and B in 7 days=\( \frac{7}{20} \)+\( \frac{7}{30} \)=\( \frac{21+14}{60} \)=\( \frac{35} {60} \)=\( \frac{7}{12} \)
So, Remaining work = 1-\( \frac{7}{12} \) =\( \frac{5}{12} \)
Time taken by C= \( \frac{12}{5} \)*10 = 24 days.

Q.37

45 men can complete a work in 16 days. Four days after they started working, 36 more men joined them. How many days will they now take to complete the remaining work ?

(1)6 days

(2)8 days

(3)6\( \frac{2}{3} \)days

(4)7\( \frac{3}{4} \)

Ans .

(3)6\( \frac{2}{3} \)days

Explanation :

Q.38

A and B together can complete a job in 8 days. Both B and C, working alone can finish the same job in 12 days. A and B commence work on the job, and work for 4 days, where upon A leaves. B continues for 2 more days, and then he leaves too. C now starts working, and finishes the job. How many days did C require ?

(1) 5

(2) 8

(3) 3

(4) 4

Ans .

(4) 4

Explanation :
(4) Work done by A and B in first 6 days
= (A + B)s 4 days work + B`s 2 days work =4*\( \frac{1}{8} \)+\( \frac{1}{12} \)
=\( \frac{1}{2} \)+\( \frac{1}{6} \)= \( \frac{3+1}{6} \) =\( \frac{2}{3} \)
Remaining work = 1-\( \frac{2}{3} \) =\( \frac{1}{3} \)
Time taken by C =\( \frac{1}{3} \)*12 = 4days.

Q.39

A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days.A alone can finish the work in

(1)60 days

(2)54 days

(3)48 days

(4)50 days

Ans .

(1)60 days

Explanation :
(1) (A + B) together do the work in 30 days
(A + B)s 1 days work =\( \frac{1}{30} \)
(A + B)s 20 days work =\( \frac{20}{30} \) =\( \frac{2}{3} \)
Remaining work =1-\( \frac{2}{3} \) = \( \frac{1}{3} \)
Time taken by A in doing \( \frac{1}{3} \) work = 20 days
Time taken in doing 1 work= 20 × 3 = 60 days.

Q.40

A, B and C can do a job in 6 days, 12 days and 15 days respectively. After\( \frac{1}{8} \) of the work is completed, C leaves the job. Rest of the work is done by A and B together. Time taken to finish the work is

(1) 5\( \frac{5}{6} \) days

(2) 5\( \frac{1}{4} \) days

(3) 3\( \frac{1}{2} \)days

(4) 3\( \frac{3}{4} \) days

Ans .

(3) 3\( \frac{1}{2} \)days

Explanation :
(3) Remaining work =1-\( \frac{1}{8} \) =\( \frac{7}{8} \)
(A + B)s 1 days work =\( \frac{1}{6} \)+\( \frac{1}{12} \)=\( \frac{2+1}{12} \)=\( \frac{3}{12} \)=\( \frac{1}{4} \)
Time taken in doing \( \frac{7}{8} \)part of work =\( \frac{7}{8} \)*4= \( \frac{7}{2} \)= 3\( \frac{1}{2} \)days

Q.41

16 women take 12 days to complete a work which can be completed by 12 men in 8 days. 16 men started working and after 3 days 10 men left and 4 women joined them. How many days will it take them to complete the remaining work ?

(1)4

(2)6

(3)8

(4)10

Ans .

(2)6

Explanation :
(2) Work done by 12 men in 8 days = Work done by 16 women in 12 days.
=> 12 × 8 men
=> 16 × 12 women
=>1 man => 2 women
Now, work done by 12 men in 1 day =\( \frac{1}{8} \)
1 mans 1 days work = \( \frac{1}{12*8} \) =\( \frac{1}{96} \)
16 mens 3 days work

Q.42

40 men can complete a work in 18 days. Eight days after they started working together, 10 more men joined them. How many days will they now take to complete the remaining work ?

(1)6

(2)8

(3)10

(4)12

Ans .

(2)8

Explanation :

Q.43

If 12 men or 24 boys can do a work in 66 days, the number of days in which 15 men and 6 boys can do it i

(1)44

(2)33

(3)55

(4)66

Ans .

(1) 44

Explanation :
12 men =24 boys
=>1 man = 2 boys
=> 15 men + 6 boys
= 30 boys + 6 boys = 36 boys
=>M₁D₁ =M₂D₂
=>24 × 66 = 36 × D₂
D₂ =\( \frac{24*66}{36} \) = 44 days.

Q.44

A, B and C together can do a piece of work in 40 days. After working with B and C for 16 days, A leaves and then B and C complete the remaining work in 40 days more. A alone could do the work in

(1) 80 days

(2) 90 days

(3) 100 days

(4) 120 days

Ans .

(3) 100 days

Explanation :
(3) A, B and C together complete the work in 40 days.
(A + B + C)s 1 days work = \( \frac{1}{40} \)
(A + B + C)s 16 days work=\(\frac{16}{40} \)=\(\frac{2}{5} \)
Remaining Work = 1-\(\frac{2}{5} \)=\(\frac{3}{5} \)
This part of work is done by B and C in 40 days.
=>Time taken in doing \(\frac{3}{5} \) work = 40 days. =>Time taken in doing in 1 work = \(\frac{40 *5}{3} \)=\(\frac{200}{3} \)days.
A`s days work = (A + B + C)s 1 days work - (B + C)s 1 days work = \(\frac{1}{40} \)+ \(\frac{3}{200} \)=\(\frac{5-3}{200} \)= \(\frac{2}{200} \)= \(\frac{1}{100} \)
Required time = 100 days.

Q.45

A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. The number of men originally was

(1) 30

(2)40

(3)32

(4)36

Ans .

(2)40

Explanation :
(2) Number of men originally = x (let)
=>M₁D₁=M₂D₂
=> × 60 = (x + 8) × 50
=>6x = 5x + 40
=>6x – 5x = 40
=>x = 40 men

Q.46

Some staff promised to do a job in 18 days, but 6 of them went on leave. So the remaining men took 20 days to complete the job.How many men were there originally ?

(1)55

(2)62

(3)56

(4)60

Ans .

(4) 60

Explanation :
(4) Using Rule 1,,
Number of men originally = x (let)
=>M₁D₁=M₂D₂
=> x × 18 = (x – 6) × 20
=>x × 9 = (x – 6) × 10
= 10x – 60
=>10x – 9x = 60
=> x = 60 men

Q.47

A certain number of men can do a piece of work in 40 days. If there were 45 men more the work could have been finished in 25 days. Find the original number of men employed in the work.

(1)70

(2)85

(3)65

(4)75

Ans .

(4)75

Explanation :
(4) Original number of men= x (let)
=>M₁D₁=M₂D₂
=>x × 40 = (x + 45) × 25
=>8x = (x + 45) × 5
=>8x = 5x + 225
=> 8x – 5x = 225
=> 3x = 225
=> x= \( \frac{225}{3} \)= 7 men.

Q.48

A and B can do a piece of work in 45 and 40 days repectively. They began the work together but A left after some days and B finished the remaining work in 23 days. A left after

(1) 6 days

(2) 9 days

(3) 12 days

(4) 5 days

Ans .

(2) 9 days

Explanation :
(2) Let A left the work after x days.
According to the question,
Work done by A in x days + work done by B in (23 + x ) days = 1
=> \( \frac{x}{45} \) +\( \frac{23+x}{40} \)=1
=>\( \frac{8x+207+9x}{360} \) = 1
=>17x + 207 = 360
=> 17x = 360 – 207 = 153
=> x = \( \frac{153}{17} \) = 9days.

Q.49

20 men can do a piece of work in 18 days, They worked together for 3 days, then 5 men joined them. In how many more days is the work completed ?

(1)15

(2)12

(3)14

(4)13

Ans .

(2) 12

Explanation :

Q.50

A, B and C can do a piece of work in 24, 30 and 40 days respectively. They began the work together but C left 4 days before completion of the work. In how many days was the work done ?

(1) 13

(2) 12

(3) 14

(4) 11

Ans .

(4) 11

Explanation :
(4) Let the work be completed in x days.
According to the question,
C worked for (x – 4) days.
= \( \frac{x}{24} \) +\( \frac{x}{30} \)=\( \frac{x-4}{40} \)=1
=>\( \frac{5x+4x+3(x-4)}{120} \) =1
=>\( \frac{12x-12}{120} \) = 1
=>\( \frac{12(x-1)}{120} \)= 1
=>\( \frac{x-1}{10} \) =>x – 1 = 10
=> x = 10 + 1 = 11 days.

Q.51

A and B can do a piece of work in 15 days. B and C can do a similar work in 12 days and C and A in 10 days. How many days will A take to do the work by himself ?

(1)13

(2)24

(3)40

(4)8

Ans .

(2)24

Explanation :
(2) (A + B)s 1 days work = \( \frac{1}{15} \)....(i)
(B + C)s 1 days work = \( \frac{1}{12} \) .... (ii) and (C + A)s 1 days work = \( \frac{1}{10} \).... (iii)
On adding all three equations, 2 (A + B + C)’s 1 days work = \( \frac{1}{15} \)+\( \frac{1}{12} \)+\( \frac{1}{10} \)
=\( \frac{4+6+5}{60} \) =\( \frac{15}{60} \) = \( \frac{1}{4} \)
(A + B + C)s 1 days work = \( \frac{1}{8} \)....(iv)
By equation (iv) – (ii), A`s 1 days work = \( \frac{1}{8} \)- \( \frac{1}{12} \) = \( \frac{3-2}{24} \) = \( \frac{1}{24} \)
Required time = 24 days.

Q.52

A certain number of men can do a work in 40 days. If there were 8 men more, it could be finished in 10 days less. How many men were there initially?

(1)20

(2)24

(3)30

(4)16

Ans .

(2)24

Explanation :
(2) Number of men initially = x (let)
=>M₁D₁=M₂D₂
=> x × 40 = (x + 8) × 30
=>4x = 3x + 24
=>4x – 3x = 24
=>x = 24 men

Q.53

X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in:

(1)18 days

(2)27 days

(3)36 days

(4)42 days

Ans .

(3) 36 days

Explanation :
(3) Let Y alone complete the work in x days.
According to the question,
X`s 16 days work + Y`s 12 days work = 1
=> \( \frac{16}{24} \) +\( \frac{12}{x} \) =1
=>\( \frac{2}{3} \) +\( \frac{12}{x} \) =1
=>\( \frac{12}{x} \) = 1 -\( \frac{2}{3} \) =\( \frac{1}{3} \)
=>x = 12 × 3 = 36 days

Q.54

12 men can complete a work in 90 days. 30 days after they started work, 2 men left and 8 men joined. How many days will it take to complete the remaining work ?

(1)90 days

(2)60 days

(3)40 days

(4)50 days

Ans .

(3)40 days

Explanation :

Q.55

A can do a job in 10 days and B can do the same job in 15 days. They start working together, but B leaves after 5 days. How many more days A want to finish the work ?

(1)2 days

(2)1\( \frac{2}{3} \)days

(3)3 days

(4)2\( \frac{2}{3} \) days

Ans .

(2)1\( \frac{2}{3} \)days

Explanation :
(2) Work done by A and B in 5 =5(\( \frac{1}{10} \)+\( \frac{1}{15} \)) =5(\( \frac{3+2}{30} \))
= 5*\( \frac{5}{30} \) =\( \frac{5}{6} \)
Remaining Work = 1- \( \frac{5}{6} \) =\( \frac{1}{6} \)
Time taken by A =\( \frac{1}{6} \)*10 = \( \frac{5}{3} \) days.=1\( \frac{2}{3} \) days.

Q.56

A and B together can finish a work in 30 days. They worked on it for 20 days and then B left the work. The remaining work was done by A alone in 20 days more. In how many days can A alone finish the work

(1)48 days

(2)50 days

(3)54 days

(4)60 days

Ans .

(4)60 days

Explanation :
(4) (A + B)’s 1 day’s work = \( \frac{1}{30} \)
(A + B)s 20 days’ work =\( \frac{20}{30} \) =\( \frac{2}{3} \)
Remaining Work =1- \( \frac{2}{3} \) =\( \frac{1}{3} \)
Time taken by A in doing \( \frac{1}{3} \) of work = 20 days
Time taken by A in doing whole work = 3 × 20 = 60 days

Q.57

Ram and Hari can cut 12 kgs nuts in 2 days. After 5 days, Hari left the work. Ram took 8 more days to cut the rest of the nuts. If total of 58 kgs of nuts were cut, the time taken by Hari to cut 10 kgs of nuts is

(1)1 days

(2)2 days

(3)3 days

(4)4 days

Ans .

(4)4 days

Explanation :
(4) Nuts cut by Ram and Hari in 1 day =\( \frac{12}{2} \)kg. = 6 kg. ....(i)
Nuts cut by them in 5 days = 30 kg.
Amount of nuts cut by Ram alone = 58 – 30 = 28 kg.
Time = 8 days
Nuts cut by Ram in 1 day =\( \frac{28}{8} \) = 3.5 kg.
From equation (i),
Nuts cut by Hari in 1 day = (6 – 3.5) kg. = 2.5 kg.
Time taken by Hari in cutting 10 kg. of nuts = \( \frac{10}{2.5} \)= 4 days

Q.58

Ramesh and Rahman can do a work in 20 and 25 days respectively. After doing collectively for 10 days at the work, they leave the work due to illness and Suresh completes rest of the work in 3 days. How many days Suresh alone can take to complete the whole work ?

(1)32 days

(2)28 days

(3)29 days

(4)30 days

Ans .

(4)30 days

Explanation :
(4) Ramesh`s 1 days work =\( \frac{1}{20} \)
Rahman`s 1 days work = \( \frac{1}{25} \)
(Ramesh + Rahman)s 1 days work = \( \frac{1}{20} \)+\( \frac{1}{25} \)= \( \frac{5+4}{100} \)=\( \frac{9}{100} \)
Their 10 days work =\( \frac{90}{100} \)=\( \frac{9}{10} \)
Remaininf Work = 1- \( \frac{9}{10} \) =\( \frac{1}{10} \)
Suresh does\( \frac{1}{10} \) work in 3 days.
Time taken by Suresh in doing 1 work = 3 × 10 = 30 days

Q.59

A can do a piece of work in 10 days and B can do it in 12 days. They work together for 3 days. Then B leaves and A alone continues. 2 days after that C joins and the work is completed in 2 days more. In how many days can C do it, if he works alone ?

(1)30 days

(2)50 days

(3)40 days

(4)60 days

Ans .

(3) 40 days

Explanation :
(3) Let C alone complete the work in x days.
According to the question,
A`s 7 days work + B`s 3 days work + C`s 2 days work = 1
=> \( \frac{7}{10} \)+\( \frac{3}{12} \)+\( \frac{2}{x} \) =1
=>\( \frac{2}{x} \)= 1 -\( \frac{7}{10} \)-\( \frac{1}{4} \)
=>\( \frac{20-14-5}{20} \) =\( \frac{1}{20} \)
=> x = 2 × 20 = 40 days.

Q.60

A certain number of men can do a piece of work in 60 days. If there were 6 men more, the work can be finished 20 days earlier. The number of men working is :

(1) 6

(2) 12

(3) 18

(4) 24

Ans .

(2) 12

Explanation :
(2) Let the number of working men be x.
=> M₁D₁=M₂D₂
=> x × 60 = (x + 6) × 40

=> 3x = 2x + 12
=> 3x – 2x = 12
=> x = 12

Q.61

A can do a piece of work in 20 days and B in 15 days. With the help of C, they finish the work in 5 days. C can alone do the work in

(1)5 days

(2)6 days

(3)10 days

(4) 12 days

Ans .

(4) 12 days

Explanation :
. (4) A`s 1 days work =\( \frac{1}{20} \)
B`s 1 days work =\( \frac{1}{15} \)
(A + B + C)s 1 days work =\( \frac{1}{5} \)
C`s 1 day`s work =\( \frac{1}{5} \)-\( \frac{1}{20} \)-\( \frac{1}{15} \)
=\( \frac{12-3-4}{60} \)=\( \frac{5}{60} \)=\( \frac{1}{12} \)
Required time = 12 days.

Q.62

15 men can finish a piece of work in 40 days. The number of days after which 5 men should leave the work so that the work is finished in 45 days altogether is :

(1)10

(2)20

(3)30

(4)35

Ans .

(3)30

Explanation :
. (3) Let 5 men leave the work after x days.
=>M₁D₁=M₂D₂+M₃D₃
=>15 × 40 = 15 × x + 10 × (45 – x)
=> 600 = 15x + 450 – 10x
=> 600 – 450 = 5x
=> 5x = 150
=> x =\( \frac{150}{5} \)= 30 days.

Q.63

A and B together can complete a piece of work in 12 days. They worked together for 5 days and then A alone finished the rest of the work in 14 days. A alone can complete the work in

(1)24 days

(2)22 days

(3)20 days

(4)18days

Ans .

(1)24days

Explanation :
(1)(A + B)s 1 days work =\( \frac{1}{12} \)
(A + B)’s 5 days’ work = \( \frac{5}{12} \)
Remaining work = 1- \( \frac{5}{12} \) = \( \frac{7}{12} \)
A does\( \frac{7}{12} \) work in 14 days.
A will do 1 work in =\( \frac{14*12}{7} \)= 24 days.

TYPE-III

Q.1

If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same in 2 days, then the time taken by 15 men and 20 boys to do the same type of work will be :

(1) 5 days

(2) 4 days

(3) 6 days

(4) 7 days

Ans .

(2) 4 days

Explanation :
(3) According to question, (6M + 8B)10 = (26M + 48B)2
60M + 80B = 52M + 96B or, 1M = 2B ; 5M + 20B = (30 + 20)B = 50 boys and 6M + 8B => (12 + 8) boys = 20 boys
20 boys can finish the work in 10 days, 50 boys can finish the work in \( \frac{20*10}{50} \) days = 4 days

Q.2

5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it ?

(1) 4 days

(2) 5 days

(3) 6 days

(4) 8 days

Ans .

(2) 5 days

Explanation :
(2) 5*6 men = 10*5 women => 3 men = 5 women;
5 women + 3 men = 6 men; 5 men complete the work in 6 days
6 men will complete the work in \( \frac{5*6}{6} \) = 5 days.

Q.3

If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?

(1) 4 days

(2) 5 days

(3) 3 days

(4) 2 days

Ans .

(3) 3 days

Explanation :
. (3) 3m = 6w => 1m = 2w; 12m + 8w = (12*2w) + 8w = 32w;
6 women can do the work in 16 days
32 women can do the work in \( \frac{16*6}{32} \) = 3 days

Q.4

A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in \( \frac{1}{4} \) of a day?

(1) 1 day

(2) 4 days

(3) 19 days

(4) 41 days

Ans .

(4) 41 days

Explanation :
. (4) 1 mans 1 days work = \( \frac{1}{3} \) 1 womans 1 days work = \( \frac{1}{4} \)
1 boys 1 days work = \( \frac{1}{4} \)
(1 man + 1 woman)s days work = \( \frac{1}{4} \)*[\( \frac{1}{3} \) + \( \frac{1}{4} \)] =\( \frac{7}{48} \)
Remaining work = 1-\( \frac{7}{48} \)=\( \frac{41}{48} \). Now;
1 boys \( \frac{1}{4} \) days work = \( \frac{1}{4} \)*\( \frac{1}{12} \)= \( \frac{1}{48} \)
\( \frac{41}{48} \) work will be done by \( \frac{41}{48} \)*48 = 41 boys

Q.5

If 16 men or 20 women can do a piece of work in 25 days. In what time will 28 men and 15 women do it?

(1) 14\( \frac{2}{7} \) day

(2) 33\( \frac{1}{3} \) days

(3) 18\( \frac{3}{4} \) days

(4) 10 days

Ans .

(4) 10 days

Explanation :
4) 16 men = 20 women => 4 men = 5 women. Now, according to question, 16 men complete the work in 25 days.
1 man one days work = \( \frac{1}{25*16} \) => 4 men one days work = \( \frac{4}{25*16} \) = \( \frac{1}{100} \). Similarly,
1 woman one days work = \( \frac{1}{25*20} \) => 5 women one days work = \( \frac{5}{25*20} \) = \( \frac{1}{100} \) => 28 men
= \( \frac{28}{4} \)*5 = 35 women => [28 men + 15 women] => 50 women one days work = \( \frac{50}{25*20} \) = \( \frac{1}{10} \)
Therefore, 28 men and 15 women can complete the whole work in 10 days.

Q.6

If 5 men or 8 women can do a piece of work in 12 days, how many days will be taken by 2 men and 4 women to do the same work?

(1) 15 days

(2) 13\( \frac{1}{2} \) days

(3) 13\( \frac{1}{3} \) days

(4) 10 days

Ans .

(3) 13\( \frac{1}{3} \) days

Explanation :
(3) According to the question, 5 men = 8 women
2 men = \( \frac{8}{5} \)*2 = \( \frac{16}{5} \)
Total women = \( \frac{16}{5} \)+4 = \( \frac{36}{5} \)
No. of days to do the same work = \( \frac{8*12*5}{36} \) = \( \frac{40}{3} \) = 13\( \frac{1}{3} \)

Q.7

If 3 men or 4 women can plough a field in 43 days, how long will 7 men and 5 women take to plough it ?

(1) 10 days

(2) 11 days

(3) 9 days

(4) 12 days

Ans .

(4) 12 days

Explanation :
(4) 3 men = 4 women
1 man = \( \frac{4}{3} \) women
7 men = \( \frac{7*4}{3} \) = \( \frac{28}{3} \)
7 men + 5 women = \( \frac{28}{3} \)+5 = \( \frac{28+15}{3} \) = \( \frac{43}{3} \) Women
Now, M₁D₁ = M₂D₂ => 4 * 43 = \( \frac{43}{3} \)*D₂, where D₂ = number of days
=> D₂ = \( \frac{4*3*43}{43} \) = 12 days.

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