- Staff Selection Commission Mathematics 1999 to 2017 - TIME AND WORK Part 4

# Staff Selection Commission Mathematics - TIME AND WORK TYPE-III

Ans .

(2)20

1. Explanation :

(2) Using Rule 1,
Let the original number of carpenters be x.
=>M1D1=M2D2
=>x * 9 = (x-5) * 12
=>9x = 12x-60
=>3x = 60 => x = 20

Ans .

(2)16 days

1. Explanation :

(2) Using Rule 1,
=>2 men + 3 women = 4 men => 2 men = 3 women \ 3 men + 3 women = 5 men =>M1D1=M2D2
=> 4 * 20 = 5 *D2
=>D2=$$\frac{4*20}{5}$$ =16 days.

Ans .

(1)12 hours

1. Explanation :

Ans .

(4)3 days

1. Explanation :

Ans .

(4)8

1. Explanation :

=> $$\frac{9}{10}$$=$$\frac{(x-1)(x+1)}{(x+2)(x-1))}$$=$$\frac{x+1}{x+2}$$
=>10x + 10 = 9x + 18
=> x = 18-10 = 8

Ans .

(3)8 hrs.

1. Explanation :

(3) Using Rule 1,
=>M1D1T1=M2D2T2
=>80*16*6 = 64*15*T2
=>T2 =$$\frac{80*16*6}{64*15}$$=8 hours.

Ans .

(1)16 days

1. Explanation :

(1) Using Rule 1,
=>M1D1=M2D2
=>18 * 24 = 27 * D2
D2=$$\frac{18*24}{27}$$= 16 days.

Ans .

(3)43$$\frac{7}{11}$$ hours

1. Explanation :

Ans .

(3)x2/y days

1. Explanation :

(3) Using Rule 1,
=>M1D1= M2D2
=> x.x = y.D2
=>D2= x2/y days.

Ans .

(2)15 days

1. Explanation :

Using Rule 1,
=>M1D1= M2D2
=> 30 * 18 = 36 * D2
=>D2= $$\frac{30*18}{36}$$ = 15 days.

Ans .

(1)10 days

1. Explanation :

1) 20 men = 24 women
=> 5 men = 6 women
=> 30 men + 12 women
= 40 men
=>M1D1= M2D2
=> 20 * 20 = 40 * D2
D2=$$\frac{20*20}{40}$$= 10 days.

Ans .

(3)34 days

1. Explanation :

Ans .

(4)20 days

1. Explanation :

(4) 3 * 5 men + 7 * 5 women
= 4 * 4 men + 6 * 4 women
=> 16 men - 15 men = 35 women - 24 women
=>1 man = 11 women
=> 3 men + 7 women = 40 women
=>M1D1= M2D2
=> 40 * 5 = 10 * D2
=>D2 = 20 days.

Ans .

(4)30

1. Explanation :

Ans .

(2)100

1. Explanation :

(2) Using Rule 1,
200 men do $$\frac{1}{4}$$ work in 50 days.

Ans .

(2)56

1. Explanation :

Ans .

(2)$$\frac{125}{49}$$

1. Explanation :

Ans .

(1)300

1. Explanation :

(1) Using Rule 1,
=>M1D1 =M2D2
=>75 * 90 = M2*18
=>M2=$$\frac{75*90}{18}$$=375
=> Number of additional men = 375-75 = 300.

Ans .

(3)5 days

1. Explanation :

(*) 4 men = 8 women
=> 1 man = 2 women
=> 6 men + 12 women
=> 12 women + 12 women = 24 women
=>M1D1 =M2D2
=> 8 * 15 = 24 * D2
=>D2 =$$\frac{8*15}{24}$$= 5days.

Ans .

(1)8

1. Explanation :

=>M1D1 =M2D2
=>24 * 17 = M2*51
=>M2 =$$\frac{24*17}{51}$$ =8 men.

# TYPE-VII

Ans .

(2)₹60

1. Explanation :

2) Ratio of Sumans and Sumatis 1 days work = $$\frac{1}{3}$$:$$\frac{1}{2}$$ =2:3
Sum of the ratios = 2 + 3 = 5
Sumans share =$$\frac{2}{5}$$*150=₹60.

Ans .

(2)₹200.20

1. Explanation :

(2) Total wages of 500 workers = 500 × 200 = 100000
Now, according to question,
Correct Average =$$\frac{100000-180-20+80+220}{500}$$
=> $$\frac{100100}{500}$$ =₹200.20.

Ans .

(3)₹750

1. Explanation :

(3) Using Rule 25,
Cs 1 days work =$$\frac{1}{4}$$-($$\frac{1}{8}$$+$$\frac{1}{12}$$)=$$\frac{1}{4}$$-($$\frac{3+2}{24}$$)
=>$$\frac{1}{4}$$-$$\frac{5}{24}$$=$$\frac{6-5}{24}$$=$$\frac{1}{24}$$
=>A : B : C =$$\frac{1}{8}$$:$$\frac{1}{12}$$:$$\frac{1}{24}$$=3:2:1
=> C's share =₹($$\frac{1}{6}$$*4500)=₹750.

Ans .

(3)₹9450

1. Explanation :

Ans .

(2)₹400

1. Explanation :

(2) Using Rule 25,
As 1 days work =$$\frac{1}{6}$$
Bs 1 days work =$$\frac{1}{8}$$ and (A + B + C)s 1 days work =$$\frac{1}{3}$$
Cs 1days work =$$\frac{1}{3}$$-$$\frac{1}{6}$$-$$\frac{1}{8}$$=$$\frac{8-4-3}{24}$$=$$\frac{1}{24}$$
Ratio of their one day’s work respectively=$$\frac{1}{6}$$:$$\frac{1}{8}$$:$$\frac{1}{24}$$=4:3:1
Sum of the ratios = 4 + 3 + 1 = 8
=> Cs share =$$\frac{1}{8}$$*3200=₹400.

Ans .

(4)₹12,000

1. Explanation :

(4) As 1 days work =$$\frac{1}{15}$$
Bs 1 days work =$$\frac{1}{10}$$
Ratio =$$\frac{1}{15}$$:$$\frac{1}{10}$$=2:3
Sum of the ratios = 2 + 3 = 5
As share =₹($$\frac{2}{5}$$*300000) =₹12,000.

Ans .

(4)₹40

1. Explanation :

(4) Man : boy = 3 : 1
Boys share = $$\frac{1}{4}$$*800 = 200.
The daily wages of boy=₹($$\frac{200}{5}$$)=₹40.

Ans .

(2)₹250

1. Explanation :

Ans .

(2)₹600

1. Explanation :

(2) Using Rule 25,
Ratio of wages of A, B and C respectively
= 5 * 6 : 6 * 4 : 4 * 9
= 30 : 24 : 36 = 5 : 4 : 6
Amount received by A =$$\frac{5}{5+4+6}$$*1800
=$$\frac{5}{15}$$*1800=₹600.

Ans .

(3)4

1. Explanation :

(3) Total salary for 20 days= (75 × 20) = 1500
Difference = (1500 – 1140) = 360
Money deducted for 1 day’s absencefrom work= (15 + 75) = 90
Number of days he was absent =$$\frac{360}{90}$$=4 days.

Ans .

(3)₹275

1. Explanation :

(3) Using Rule 25,
First mans 1 days work =$$\frac{1}{7}$$
Second mans 1 days work =$$\frac{1}{8}$$
Let, Boys 1 days work =$$\frac{1}{x}$$
=>$$\frac{1}{7}$$+$$\frac{1}{8}$$+$$\frac{1}{x}$$=$$\frac{1}{3}$$
=>$$\frac{1}{x}$$ = $$\frac{1}{3}$$-$$\frac{1}{7}$$-$$\frac{1}{8}$$
=>$$\frac{56-24-21}{168}$$=$$\frac{11}{168}$$
=> Ratio of their one days work=$$\frac{1}{7}$$:$$\frac{1}{8}$$:$$\frac{11}{168}$$=24:21:11
=>Sum of the ratios = 24 + 21 + 11= 56
=> Boys share in wages =$$\frac{11}{56}$$*1400 =₹275.

Ans .

(4)₹17,100

1. Explanation :

(4) 5 men = 7 women
[Both earn same amount in 1 day]
7 men =$$\frac{7}{5}$$*7 =$$\frac{49}{5}$$ women
7 men + 13 women
=>$$\frac{49}{5}$$+13 =$$\frac{114}{5}$$ women
Now,7 women = 5250 => $$\frac{114}{5}$$ women
=>$$\frac{5250}{7}$$*$$\frac{114}{5}$$=₹17,100.

Ans .

(1)₹400

1. Explanation :

(1) According to the question,
(2 × 14) men + 14 women
= 16 men + 32 women
=>(28 – 16) men =(32–14) women
=> 12 men = 18 women
=> 2 men = 3 women
1 woman =$$\frac{2}{3}$$man
Amount received by 1 woman per day= $$\frac{2}{3}$$*600=₹400.

Ans .

(3)₹160

1. Explanation :

(3) Using Rule 25,
Work done by the third person in 1 day=$$\frac{1}{8}$$-$$\frac{1}{16}$$-$$\frac{1}{24}$$=$$\frac{6-3-2}{48}$$=$$\frac{1}{48}$$
Ratio of their 1 day’s work=$$\frac{1}{16}$$:$$\frac{1}{24}$$:$$\frac{1}{48}$$=3:2:1
Share of the third person =$$\frac{1}{3+2+1}$$*960=$$\frac{960}{6}$$
=>₹160.

Ans .

(1)6:5

1. Explanation :

(1) Using Rule 25,
Required ratio = 15 * 22 : 11 * 25 = 6 : 5

Ans .

(4)₹12000

1. Explanation :

(4) Experts 1 days work=$$\frac{1}{12}$$-$$\frac{1}{36}$$-$$\frac{1}{48}$$
=>$$\frac{12-4-3}{144}$$=$$\frac{5}{144}$$
Ratio of their respective work for 1 day =$$\frac{1}{36}$$:$$\frac{1}{48}$$:$$\frac{5}{144}$$=4:3:5
Experts share =$$\frac{5}{12}$$*28800=₹12000.

Ans .

(1)₹300

1. Explanation :

(1) Using Rule 25,
According to the question
$$\frac{1}{15}$$ +$$\frac{1}{12}$$ +$$\frac{1}{C}$$ =$$\frac{1}{5}$$
Let C1s work in day be $$\frac{1}{C}$$
$$\frac{1}{C}$$=$$\frac{1}{5}$$-$$\frac{1}{15}$$-$$\frac{1}{12}$$=$$\frac{12-4-5}{60}$$=$$\frac{1}{20}$$
=>A:B:C=$$\frac{1}{15}$$:$$\frac{1}{12}$$:$$\frac{1}{20}$$=4:5:3
=> Cs share =$$\frac{3}{12}$$*1200 = ₹300.

Ans .

(4)12 days

1. Explanation :

(4) As 1 days work = $$\frac{1}{21}$$
Bs 1 days work = $$\frac{1}{28}$$
Total work done by both=$$\frac{1}{21}$$+$$\frac{1}{28}$$=$$\frac{4+3}{84}$$=$$\frac{1}{12}$$
Amount is sufficient to pay 12 days wages of both.

Ans .

(4)₹400

1. Explanation :

(4) Rule 2 and Rule 25,
Work done by A and B in 5 days = 5($$\frac{1}{12}$$+$$\frac{1}{15}$$)
=5($$\frac{5+4}{60}$$)=$$\frac{9}{12}$$=$$\frac{3}{4}$$
Time taken by C in doing $$\frac{1}{4}$$work = 5 days
C will complete in 20 days.
Ratio of wages = $$\frac{1}{12}$$:$$\frac{1}{15}$$:$$\frac{1}{20}$$
=>5:4:3
Amount received by A= $$\frac{5}{12}$$*960 = ₹400

Ans .

(2)₹20

1. Explanation :

(2) The daily earning of 'C' = Daily earning of (A + C) and (B + C) - Daily earning of (A + B + C) = 94 + 76 - 150 = 20

Ans .

(3)₹225

1. Explanation :

(3) Rule 3 and Rule 25,
If the fourth person completes the work in x days, then
$$\frac{3}{8}$$+$$\frac{3}{12}$$+$$\frac{3}{16}$$+$$\frac{3}{x}$$=1
=>$$\frac{1}{x}$$ = $$\frac{1}{3}$$-$$\frac{1}{8}$$-$$\frac{1}{12}$$-$$\frac{1}{16}$$
=>$$\frac{16-6-4-3}{48}$$ =>$$\frac{1}{16}$$
x = 16
Ratio of wages =$$\frac{1}{8}$$:$$\frac{1}{12}$$:$$\frac{1}{16}$$:$$\frac{1}{16}$$=6:4:3:3
Sum of ratios = 6 + 4 + 3+3 = 16
Fourth persons share =$$\frac{3}{16}$$*1200=₹225.

Ans .

(1) A : 150, B : 100, C : 150

1. Explanation :

(1) Rule 3 and Rule 25,
If C alone completes the work in x days, then
$$\frac{1}{16}$$+$$\frac{1}{24}$$+$$\frac{1}{x}$$=$$\frac{1}{6}$$
=> $$\frac{1}{x}$$ = $$\frac{1}{6}$$-$$\frac{1}{16}$$-$$\frac{1}{24}$$
=>$$\frac{8-3-2}{48}$$=$$\frac{1}{16}$$
=>x = 16 days
Ratio of their remuneration =$$\frac{1}{16}$$:$$\frac{1}{24}$$:$$\frac{1}{16}$$= 3:2:2
As remuneration =$$\frac{3}{8}$$*400 = ₹150
Bs remuneration =$$\frac{2}{8}$$*400 =₹100
Cs remuneration =$$\frac{3}{8}$$*400 =₹150
=> A : 150, B : 100, C : 150

Ans .

(4)143.50

1. Explanation :

(4) Using Rule 25,
Skilled : half skilled : unskilled =$$\frac{1}{3}$$:$$\frac{1}{4}$$:$$\frac{1}{6}$$
=>($$\frac{1}{3}$$*12) :($$\frac{1}{4}$$*12):($$\frac{1}{6}$$*12)
= 4 : 3 : 2 Share of the trained labourer =$$\frac{28}{(7*4+8*3+2*10)}$$ *369 =$$\frac{28}{28+24+20}$$*369
=>$$\frac{28}{72}$$*369 =143.50.

Ans .

(2)₹100

1. Explanation :

(2) Work done by B= 1-$$\frac{19}{23}$$ = $$\frac{23-19}{23}$$ = $$\frac{4}{23}$$
(A + C) : B = $$\frac{19}{23}$$:$$\frac{4}{23}$$ =19:4
Sum of ratios = 19 + 4 = 23
Bs share =$$\frac{4}{23}$$*575 =₹100

Ans .

(4)5 hours

1. Explanation :

Rate of earning of the man = 2000/50 = Rs. 40 per hour
Rate of earning for additional hours = 40 × 3/2 = Rs. 60 per hour
Let the man has to work for n additional hours.
Then, 2000 + n × 60 = 2300
⇒ n × 60 = 300
⇒ n = 5h.

Ans .

(3)Rs.120

1. Explanation :

(3) (2 men + 1 woman)s 14 days work = (4 women + 2 men)s 8 days work
=> 28 men + 14 women
=> 32 women + 16 men
=> (28 - 16) = 12 men
=> (32 - 14) = 18 women
=> 2 men = 3 women
1 woman = $$\frac{2}{3}$$ man
=> Wages per day of 1 man = Rs. 180
=> Wages per day of 1 woman$$\frac{2}{3}$$*180 =Rs.120.

Ans .

(1)Rs. 67.50

1. Explanation :

(1) Time taken by A =$$\frac{63}{3.50}$$= 18 days
Time taken by B =$$\frac{75}{2.5}$$ =30 days.
(A + B)s 1 days work =$$\frac{1}{18}$$+$$\frac{1}{30}$$ = $$\frac{5+3}{90}$$ =$$\frac{8}{90}$$ = $$\frac{4}{45}$$
Required time =$$\frac{45}{4}$$ days
Total wages =$$\frac{45}{4}$$ * (3.50 + 2.50)
=>Rs($$\frac{45}{4}$$*6) = )Rs. 67.5.

Ans .

(3) Rs.250

1. Explanation :

(3) Ratio of As and Bs 1 days work =$$\frac{1}{12}$$:$$\frac{1}{15}$$ = 15:12 => 5:4
Sum of the terms of ratio = 5 + 4 = 9
As share = Rs.($$\frac{5}{9}$$*450) = Rs.250.

Ans .

(1)Rs. 200

1. Explanation :

(1) Part of work done by C
=> 1- $$\frac{7}{11}$$-$$\frac{4}{11}$$
=> Total amount received = Rs. 550
=> Cs share = Rs($$\frac{4}{11}$$*550) =Rs. 200.

Ans .

(1)Rs.50

1. Explanation :

(1) Let C alone complete the work in x days.
According to the question,
$$\frac{1}{5}$$+$$\frac{1}{15}$$+$$\frac{1}{x}$$=$$\frac{1}{3}$$
=>$$\frac{1}{x}$$ =$$\frac{1}{3}$$-$$\frac{1}{5}$$-$$\frac{1}{15}$$
=>$$\frac{5-3-1}{15}$$ =>$$\frac{1}{15}$$
\ => x = 15 days = Time taken by C alone.
Ratio of the 1 day’s work of A, B and C =$$\frac{1}{5}$$:$$\frac{1}{15}$$:$$\frac{1}{15}$$ => 3:1:1
Sum of the terms of ratio = 3 + 1 + 1 = 5
C’s share = Rs($$\frac{1}{5}$$*250) => Rs.50

Ans .

(1) Man ₹2.75, Woman ₹2.25

1. Explanation :

(1) Let daily wages of a man be Rs. x
Daily wages of a woman = Rs.(x-$$\frac{1}{2}$$)
According to the question, 600x + 400(x-$$\frac{1}{2}$$)
= 1000 × 2.55
=> 600x + 400x - 200 = 2550
=> 1000x = 2550 + 200 = 2750
=> x=$$\frac{2750}{1000}$$ =Rs. 2.75
=> Daily wages of a woman
=>Rs. (2.75 – 0.5)
=>Rs. 2.25

# TYPE-VIII

Ans .

(1) 10

1. Explanation :

(1) Let initially the number of men
be x.
=> According to question,
M1D1W2 = M2D2W1
x*30 = (x + 5)*(30 - 10)
x*30 = 20x + 100
30x - 20x = 100
10x = 100
x = 10

Ans .

(4) 8

1. Explanation :

(4) Using Rule 1,

=> 450*10*5*x
= 625*8*6*6
=> x = $$\frac{625*8*6*6}{450*10*5}$$ = 8

Ans .

(1) 24 days

1. Explanation :

(1) Work done by A in 15 days
= $$\frac{1}{60}$$*15 = $$\frac{1}{4}$$
Remaining work = 1-$$\frac{1}{4}$$ = $$\frac{3}{4}$$
Now, $$\frac{3}{4}$$ work is done by B in 30
days
Whole work will be done by B in
$$\frac{30*4}{3}$$ = 40 days
As 1 days work = $$\frac{1}{60}$$ and Bs 1
days work = $$\frac{1}{40}$$
(A + B)s 1 days work
= $$\frac{1}{60}$$+$$\frac{1}{40}$$ = $$\frac{2+3}{120}$$ = $$\frac{5}{120}$$ = $$\frac{1}{24}$$
Hence, both will finish the work in 24 days.

Ans .

(2) 25 days

1. Explanation :

(2) As 1 days work
= (B +C)s 1 days work ...(i)
(A + B)s 1 days work = $$\frac{1}{10}$$
Cs 1 days work = $$\frac{1}{50}$$
(A + B + C)s 1 days work
= $$\frac{1}{10}$$+$$\frac{1}{50}$$ = $$\frac{5+1}{50}$$ = $$\frac{6}{50}$$ = $$\frac{3}{25}$$ ...(iii)
(A + A)s 1 days work = $$\frac{3}{25}$$
(By (i) & (iii)
As 1 days work = $$\frac{3}{50}$$
Bs 1 days work = $$\frac{1}{10}$$-$$\frac{3}{50}$$
= $$\frac{5-3}{50}$$ = $$\frac{2}{50}$$ = $$\frac{1}{25}$$
Hence, B alone will complete the
work in 25 days

Ans .

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

1. Explanation :

(3) Using Rule 2,
Let the son take x days to do the
work.
$$\frac{1}{5}$$+$$\frac{1}{x}$$ = $$\frac{1}{3}$$
=> $$\frac{x+5}{5x}$$ = $$\frac{1}{2}$$
=> 3x + 15 = 5x
=> 2x = 15 => x = $$\frac{15}{2}$$ = 7$$\frac{1}{2}$$ days

Ans .

(4) 40

1. Explanation :

(4) Let the number of men in the
beginning = x
Then, $$\frac{x+8}{x}$$ = $$\frac{60}{50}$$
=> $$\frac{x+8}{x}$$ = $$\frac{6}{5}$$
=> 6x = 5x + 40 => x = 40

Ans .

(1) 192

1. Explanation :

(1) 12 persons can complete a
work in 4 days.
=> 24 persons can complete the work in 2 days.
=> 24 persons can complete the 8 times work in 16 days
=> 24*8 persons = 192 persons can complete the 8 times work in 2 days.

Ans .

(2) 110

1. Explanation :

(2) Let the original number of
workers = x. Then,
x*100 = (x -10)*110
=> 10x = 11x - 110
=> x = 110

Ans .

(3) 12 days

1. Explanation :

(3) Work done by 12 men in 6
days = $$\frac{1}{2}$$
Remaining work
= 1-$$\frac{1}{2}$$ = $$\frac{1}{2}$$
6 men leave the work.
Time taken = $$\frac{12*12}{6*2}$$ = 12 days

Ans .

(2) 15

1. Explanation :

(2) Using Rule 1,
60 men can complete a work in
250 days.
Work done by 60 men in 1 day
= $$\frac{1}{250}$$
=> Work done by 60 men in 200
days = $$\frac{200}{250}$$ = $$\frac{4}{5}$$
Remaining work = 1-$$\frac{4}{5}$$ = $$\frac{1}{5}$$
Work is stopped for 10 days.

Ans .

(1) 3 days

1. Explanation :

(1) Using Rule 2,
Working 5 hours a day, A can complete a work in 8 days.
i.e. A can complete the work in 40 hours.
Similarly, B will complete the same work in 60 hours.
(A + B)s 1 hours work
= $$\frac{1}{40}$$+$$\frac{1}{60}$$ = $$\frac{3+2}{120}$$
= $$\frac{5}{120}$$ = $$\frac{1}{24}$$
Hence, A and B together will complete the work in 24 hours.
They can complete the work in 3 days working 8 hours a day.

Ans .

(4) 2 days

1. Explanation :

(4) According to the question,
2 persons with equal abilities can do 1 job in 1 day
Time taken by 1 man to complete 1 job = 2 days
=> Time taken by 100 persons in completing 100 jobs = 2 days

Ans .

(2) 6.30 p.m.

1. Explanation :

(2) Part of the field mowed by
Ganga and Saraswati in first 2
hours
= $$\frac{1}{8}$$+$$\frac{1}{12}$$ = $$\frac{3+2}{24}$$ = $$\frac{5}{24}$$
Part of the field mowed in first
8 hours = $$\frac{5*4}{24}$$ = $$\frac{20}{24}$$ = $$\frac{5}{6}$$
Remaining work = 1 -$$\frac{5}{6}$$ = $$\frac{1}{6}$$
Now, it is the turn of Ganga, part
of work done by Ganga in 1 hour = $$\frac{1}{8}$$
Remaining work = $$\frac{1}{6}$$-$$\frac{1}{8}$$ = $$\frac{1}{24}$$
Now, time taken by Saraswati in
completing this part of work
= $$\frac{1}{24}$$*12 = $$\frac{1}{2}$$ hour
Total time = 9*$$\frac{1}{2}$$ hour
The mowing starts at 9 am.
Hence, the mowing will be completed
at 6.30 pm.

Ans .

(3) 200

1. Explanation :

(3) Using Rule 1,
Remaining work
= 5-$$\frac{7}{2}$$ = $$\frac{3}{2}$$
M1D1W2 = M2D2W1
=> 280*80*$$\frac{3}{2}$$ = M2*20*$$\frac{7}{2}$$
=> M2 = $$\frac{280*80*30}{20*7}$$ = 480
Required number of additionalmen = 480 - 280 = 200

Ans .

(1) 6 days

1. Explanation :

(1) Let B alone do the work in x
days.
6*$$\frac{1}{12}$$ + 3*$$\frac{1}{x}$$ = 1
=> $$\frac{1}{2}$$+$$\frac{3}{x}$$ = 1
$$\frac{3}{x}$$ = $$\frac{1}{2}$$ => x = 6 days

Ans .

(4) 4:3

1. Explanation :

(4) Using Rule 15,
Efficiency and time taken are inversely
proportional.
Required ratio = 4:3

Ans .

(3) 75

1. Explanation :

(3) Scheduled time to complete the
work = 40 days
25 men in 24 days do $$\frac{1}{3}$$ work
1 man in 1 day does $$\frac{1}{3*25*24}$$ = $$\frac{1}{1800}$$ work
Work remaining = 1-$$\frac{1}{3}$$ = $$\frac{2}{3}$$
The work is to be completed 4
days before schedule i.e.,
in (40 - 4) = 36 days
No. of days left for $$\frac{2}{3}$$rd work
= 36 - 24 = 12 days
$$\frac{1}{1800}$$ work is done in 1 day by
1 man.
$$\frac{2}{3}$$rd work will be done in 12 days
by
1800*$$\frac{2}{3}$$*$$\frac{1}{12}$$ = 100 men
Extra men to be employed
= 100 - 25 = 75

Ans .

(2) 4:3

1. Explanation :

(2) 20*16 women
= 16*15 men
=> 4 women = 3 men
=> $$\frac{men}{women}$$ = $$\frac{4}{3}$$
Hence, working capacity of man :
woman = 4:3

Ans .

(1) 45 days

1. Explanation :

(1) Man : Woman (efficiency)
= 3:2
i.e., Woman completes $$\frac{2}{5}$$
th work in 18 days.
Time taken by the woman to
complete the whole work = $$\frac{18*5}{2}$$ = 45 days

Ans .

(1) 3y:2x

1. Explanation :

(1) 1 mans 1 days work = $$\frac{1}{2x}$$
1 womans 1 days work = $$\frac{1}{3y}$$
Required ratio = $$\frac{1}{2x}$$ $$\frac{1}{3y}$$
= 3y:2x

Ans .

(2) 9 hrs

1. Explanation :

(2) Using Rule 1,
D1T1 = DT2
=> 18*6 = 12*T2
=> T2 = $$\frac{18*6}{12}$$ = 9 hrs

Ans .

(3) 138

1. Explanation :

(3) Using Rule 1,

=> 12*6*240*x = 18*8*36*460
=> x = $$\frac{18*8*36*460}{12*6*240}$$ = 138

Ans .

(3) 30

1. Explanation :

(3) Using Rule 1,

=> 18*2*12*6*8x = 32*3*9*9*10*8
=> x = $$\frac{32*3*9*9*10*8}{18*2*12*6*8}$$ = 30 days

Ans .

(2) 10

1. Explanation :

(2) (P + Q)s 1 days work = $$\frac{1}{6}$$
(Q + R)s 1 days work = $$\frac{7}{60}$$
Let P alone do the work in x
days.
According to the question,
$$\frac{3}{x}$$+$$\frac{6*7}{60}$$ = 1
=> $$\frac{3}{x}$$ = 1-$$\frac{7}{10}$$ = $$\frac{3}{10}$$
=> x = 10 days
Qs 1 days work = $$\frac{1}{6}$$-$$\frac{1}{10}$$ = $$\frac{1}{15}$$
Rs 1 days work = $$\frac{7}{60}$$-$$\frac{1}{15}$$ = $$\frac{1}{20}$$
Time taken by R = 20 days
Required answer = 20 - 10
= 10 days

Ans .

(3) 25

1. Explanation :

(3) Let 150 workers complete the
work in x days.
150*x = 150 + 146 + .... to (x + 8) terms
On putting x = 17
LHS = 150*17 = 2550
RHS = 150 + 146 + .... to 25 terms
a = 150, d = - 4, n = 25
S = $$\frac{n}{2}$$*[2a+(n-1)d]
= $$\frac{25}{2}$$*[2*150 + 24*(-4)]
= $$\frac{25}{2}$$*(300-96) = 2550
Note : It is better to solve by options.

Ans .

(1) 20

1. Explanation :

(1) Using Rule 1,
According to the question,
M1D1 = M2D2
=>(x + 4)*(x + 5)
= (x - 5)*(x + 20)
=> x2 + 5x + 4x + 20
= x2 - 5x + 20x - 100
=> 9x + 20 = 15x - 100
=> 15x - 9x = 100 + 20
=> 6x = 120 => x = 20

Ans .

(3) 10 days

1. Explanation :

(3) Let the work be finished in x
days.
$$\frac{x}{50}$$+$$\frac{x-1}{50}$$+$$\frac{x-2}{50}$$+ ... + $$\frac{1}{50}$$ = 1
=> x + x - 1 + x - 2 + .... + 1 = 50
i.e., 10 + 9 + 8 + .... + 1
= 55
9 + 8 + .... + 1 = 45
Required time = 10 days

Ans .

(3) 10

1. Explanation :

(3)

=> 48*7*x = 20*21*8
=> x = $$\frac{20*21*8}{48*7}$$ => x = 10

Ans .

(2) 6$$\frac{10}{33}$$ days

1. Explanation :

(2) Area of the four walls and ceiling
of the room
= 2h (l + b) + lb
= 2*10 (25 + 12) + 25*12
= (20*37 + 300) sq. metre
= (740 + 300) sq. metre
= 1040 sq. metre
Area painted by A in 1 day
= $$\frac{250}{2}$$ = 125 sq. metre
Area painted by both in1 day
= (125 + 40) sq. metre
= 165 sq. metre
Required time = $$\frac{1040}{165}$$ = $$\frac{208}{33}$$ = 6$$\frac{10}{33}$$ days

Ans .

(1) 54

1. Explanation :

(1) Here, the length of wall is
same in both cases.
M1D1 = M2D2
=> 36*21 = M2*14
=> M2 = $$\frac{36*21}{14}$$ = 54 days

Ans .

(2) 488 kg.

1. Explanation :

(2) Number of days in April and
May = 30 + 31 = 61
Q Requirement of rice for 7 days = 56 kg.
Requirement of rice for 61 days
= $$\frac{56}{7}$$*61 = 488 kg.

Ans .

(1) 40 minutes

1. Explanation :

(1) Total working time of school
= (45*8) minutes
= 360 minutes
If 9 periods are held per day,
Working time of each period
$$\frac{360}{9}$$ = 40 minutes

Ans .

(3) 7

1. Explanation :

Ans .

(2) 45.

1. Explanation :

# TEST YOURSELF

Ans .

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

1. Explanation :

Ans .

(4) 8 days

1. Explanation :

Ans .

(2)120 days

1. Explanation :

(2) According to the question Work done by A and B together in one day =$$\frac{1}{10}$$ part
Work done by B and C together

Ans .

(1)42

1. Explanation :

(1) Using Rule 1,

Ans .

(2)RS.163.04

1. Explanation :

(2) Using Rule 1,
Amount received by Meeta =$$\frac{6}{23}$$*625 = Rs. 163.04

Ans .

(1)35

1. Explanation :

Ans .

(1)4 $$\frac{4}{5}$$day

1. Explanation :

(1) As one days work =$$\frac{1}{12}$$
B`s one days work =$$\frac{1}{8}$$
(A + B)s one days work=$$\frac{1}{12}$$+$$\frac{1}{8}$$ =$$\frac{2+3}{24}$$ =$$\frac{5}{24}$$
Now,$$\frac{5}{24}$$ work is done in 1day
1 work is done in = $$\frac{24}{5}$$days =4 $$\frac{4}{5}$$ days.

Ans .

(2)9 days

1. Explanation :

Ans .

(3)12 days

1. Explanation :

Ans .

(4)30 days

1. Explanation :

Ans .

(1)36 days

1. Explanation :

Ans .

(2)15 days

1. Explanation :

Ans .

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

1. Explanation :

Ans .

(4)9 days

1. Explanation :

Ans .

(1)40 days

1. Explanation :

Ans .

(2)24 days

1. Explanation :

Ans .

(3)18 days

1. Explanation :

Ans .

(4)15 days

1. Explanation :

Ans .

(1)20 days

1. Explanation :

Ans .

(2)16.5 days

1. Explanation :

Ans .

(3)240 days

1. Explanation :