**Ans . **

(2)20

**Explanation :**(2) Using Rule 1,

Let the original number of carpenters be x.

=>M_{1}D_{1}=M_{2}D_{2}

=>x * 9 = (x-5) * 12

=>9x = 12x-60

=>3x = 60 => x = 20

**Ans . **

(2)16 days

**Explanation :**(2) Using Rule 1,

=>2 men + 3 women = 4 men => 2 men = 3 women \ 3 men + 3 women = 5 men =>M_{1}D_{1}=M_{2}D_{2}

=> 4 * 20 = 5 *D_{2}

=>D_{2}=\( \frac{4*20}{5} \) =16 days.

**Ans . **

(1)12 hours

**Explanation :**

**Ans . **

(4)3 days

**Explanation :**

**Ans . **

(4)8

**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.

**Explanation :**(3) Using Rule 1,

=>M_{1}D_{1}T_{1}=M_{2}D_{2}T_{2}

=>80*16*6 = 64*15*T_{2}

=>T_{2}=\( \frac{80*16*6}{64*15} \)=8 hours.

**Ans . **

(1)16 days

**Explanation :**(1) Using Rule 1,

=>M_{1}D_{1}=M_{2}D_{2}

=>18 * 24 = 27 * D_{2}

D_{2}=\( \frac{18*24}{27} \)= 16 days.

**Ans . **

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

**Explanation :**

**Ans . **

(3)x^{2}/y days

**Explanation :**(3) Using Rule 1,

=>M_{1}D_{1}= M_{2}D_{2}

=> x.x = y.D_{2}

=>D_{2}= x^{2}/y days.

**Ans . **

(2)15 days

**Explanation :**Using Rule 1,

=>M_{1}D_{1}= M_{2}D_{2}

=> 30 * 18 = 36 * D_{2}

=>D_{2}= \( \frac{30*18}{36} \) = 15 days.

**Ans . **

(1)10 days

**Explanation :**1) 20 men = 24 women

=> 5 men = 6 women

=> 30 men + 12 women

= 40 men

=>M_{1}D_{1}= M_{2}D_{2}

=> 20 * 20 = 40 * D_{2}

D_{2}=\( \frac{20*20}{40} \)= 10 days.

**Ans . **

(3)34 days

**Explanation :**

**Ans . **

(4)20 days

**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

=>M_{1}D_{1}= M_{2}D_{2}

=> 40 * 5 = 10 * D_{2}

=>D_{2}= 20 days.

**Ans . **

(4)30

**Explanation :**

**Ans . **

(2)100

**Explanation :**(2) Using Rule 1,

200 men do \( \frac{1}{4} \) work in 50 days.

**Ans . **

(2)56

**Explanation :**

**Ans . **

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

**Explanation :**

**Ans . **

(1)300

**Explanation :**(1) Using Rule 1,

=>M_{1}D_{1}=M_{2}D_{2}

=>75 * 90 = M_{2}*18

=>M_{2}=\( \frac{75*90}{18} \)=375

=> Number of additional men = 375-75 = 300.

**Ans . **

(3)5 days

**Explanation :**(*) 4 men = 8 women

=> 1 man = 2 women

=> 6 men + 12 women

=> 12 women + 12 women = 24 women

=>M_{1}D_{1}=M_{2}D_{2}

=> 8 * 15 = 24 * D_{2}

=>D_{2}=\( \frac{8*15}{24} \)= 5days.

**Ans . **

(1)8

**Explanation :**=>M

_{1}D_{1}=M_{2}D_{2}

=>24 * 17 = M_{2}*51

=>M_{2}=\( \frac{24*17}{51} \) =8 men.

**Ans . **

(2)₹60

**Explanation :**2) Ratio of Suman`s and Sumati`s 1 days work = \( \frac{1}{3} \):\( \frac{1}{2} \) =2:3

Sum of the ratios = 2 + 3 = 5

Suman`s share =\( \frac{2}{5} \)*150=₹60.

**Ans . **

(2)₹200.20

**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

**Explanation :**(3) Using Rule 25,

C`s 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

**Explanation :**

**Ans . **

(2)₹400

**Explanation :**(2) Using Rule 25,

A`s 1 days work =\( \frac{1}{6} \)

B`s 1 days work =\( \frac{1}{8} \) and (A + B + C)s 1 days work =\( \frac{1}{3} \)

C`s 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

=> C`s share =\( \frac{1}{8} \)*3200=₹400.

**Ans . **

(4)₹12,000

**Explanation :**(4) A`s 1 days work =\( \frac{1}{15} \)

B`s 1 days work =\( \frac{1}{10} \)

Ratio =\( \frac{1}{15} \):\( \frac{1}{10} \)=2:3

Sum of the ratios = 2 + 3 = 5

A`s share =₹(\( \frac{2}{5} \)*300000) =₹12,000.

**Ans . **

(4)₹40

**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

**Explanation :**

**Ans . **

(2)₹600

**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

**Explanation :**(3) Total salary for 20 days= (75 × 20) = 1500

Actual salary received = 1140

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

**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

=> Boy`s share in wages =\( \frac{11}{56} \)*1400 =₹275.

**Ans . **

(4)₹17,100

**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

**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

**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

**Explanation :**(1) Using Rule 25,

Required ratio = 15 * 22 : 11 * 25 = 6 : 5

**Ans . **

(4)₹12000

**Explanation :**(4) Expert`s 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

**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

=> C`s share =\( \frac{3}{12} \)*1200 = ₹300.

**Ans . **

(4)12 days

**Explanation :**(4) A`s 1 days work = \( \frac{1}{21} \)

B`s 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

**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

**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

**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 person`s share =\( \frac{3}{16} \)*1200=₹225.

**Ans . **

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

**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

A`s remuneration =\( \frac{3}{8} \)*400 = ₹150

B`s remuneration =\( \frac{2}{8} \)*400 =₹100

C`s remuneration =\( \frac{3}{8} \)*400 =₹150

=> A : 150, B : 100, C : 150

**Ans . **

(4)143.50~~
~~

**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

**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

B`s share =\( \frac{4}{23} \)*575 =₹100

**Ans . **

(4)5 hours

**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

**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

**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

**Explanation :**(3) Ratio of A`s and B`s 1 days work =\( \frac{1}{12} \):\( \frac{1}{15} \) = 15:12 => 5:4

Sum of the terms of ratio = 5 + 4 = 9

A`s share = Rs.(\( \frac{5}{9} \)*450) = Rs.250.

**Ans . **

(1)Rs. 200

**Explanation :**(1) Part of work done by C

=> 1- \( \frac{7}{11} \)-\( \frac{4}{11} \)

=> Total amount received = Rs. 550

=> C`s share = Rs(\( \frac{4}{11} \)*550) =Rs. 200.

**Ans . **

(1)Rs.50

**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

**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

**Ans . **

(1) 10

**Explanation :**(1) Let initially the number of men

be x.

=> According to question,

M_{1}D_{1}W_{2}= M_{2}D_{2}W_{1}

x*30 = (x + 5)*(30 - 10)

x*30 = 20x + 100

30x - 20x = 100

10x = 100

x = 10

**Ans . **

(4) 8

**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

**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

**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

**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

**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

**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

**Explanation :**(2) Let the original number of

workers = x. Then,

x*100 = (x -10)*110

=> 10x = 11x - 110

=> x = 110

**Ans . **

(3) 12 days

**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

**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

**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

**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.

**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

**Explanation :**(3) Using Rule 1,

Remaining work

= 5-\( \frac{7}{2} \) = \( \frac{3}{2} \)

M_{1}D_{1}W_{2}= M_{2}D_{2}W_{1}

=> 280*80*\( \frac{3}{2} \) = M_{2}*20*\( \frac{7}{2} \)

=> M_{2}= \( \frac{280*80*30}{20*7} \) = 480

Required number of additionalmen = 480 - 280 = 200

**Ans . **

(1) 6 days

**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

**Explanation :**(4) Using Rule 15,

Efficiency and time taken are inversely

proportional.

Required ratio = 4:3

**Ans . **

(3) 75

**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

25 men are already working

Extra men to be employed

= 100 - 25 = 75

**Ans . **

(2) 4:3

**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

**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

**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

**Explanation :**(2) Using Rule 1,

D_{1}T_{1}= D_{}T_{2}

=> 18*6 = 12*T_{2}

=> T_{2}= \( \frac{18*6}{12} \) = 9 hrs

**Ans . **

(3) 138

**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

**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

**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

**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

**Explanation :**(1) Using Rule 1,

According to the question,

M_{1}D_{1}= M_{2}D_{2}

=>(x + 4)*(x + 5)

= (x - 5)*(x + 20)

=> x^{2}+ 5x + 4x + 20

= x^{2}- 5x + 20x - 100

=> 9x + 20 = 15x - 100

=> 15x - 9x = 100 + 20

=> 6x = 120 => x = 20

**Ans . **

(3) 10 days

**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

**Explanation :**(3)

=> 48*7*x = 20*21*8

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

**Ans . **

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

**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

**Explanation :**(1) Here, the length of wall is

same in both cases.

M_{1}D_{1}= M_{2}D_{2}

=> 36*21 = M_{2}*14

=> M_{2}= \( \frac{36*21}{14} \) = 54 days

**Ans . **

(2) 488 kg.

**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

**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

**Explanation :**

**Ans . **

(2) 45.

**Explanation :**

**Ans . **

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

**Explanation :**

**Ans . **

(4) 8 days

**Explanation :**

**Ans . **

(2)120 days

**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

**Explanation :**(1) Using Rule 1,

**Ans . **

(2)RS.163.04

**Explanation :**(2) Using Rule 1,

Amount received by Meeta =\( \frac{6}{23} \)*625 = Rs. 163.04

**Ans . **

(1)35

**Explanation :**

**Ans . **

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

**Explanation :**(1) A`s 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

**Explanation :**

**Ans . **

(3)12 days

**Explanation :**

**Ans . **

(4)30 days

**Explanation :**

**Ans . **

(1)36 days

**Explanation :**

**Ans . **

(2)15 days

**Explanation :**

**Ans . **

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

**Explanation :**

**Ans . **

(4)9 days

**Explanation :**

**Ans . **

(1)40 days

**Explanation :**

**Ans . **

(2)24 days

**Explanation :**

**Ans . **

(3)18 days

**Explanation :**

**Ans . **

(4)15 days

**Explanation :**

**Ans . **

(1)20 days

**Explanation :**

**Ans . **

(2)16.5 days

**Explanation :**

**Ans . **

(3)240 days

**Explanation :**