## ANSWERS

**1.(1)**

12 men can complete the work in 36 days.

∴ 12 × 36 men can complete the work in 1 day.

Again,

18 women can complete the work 60 days

∴ 18 × 60 women can complete the work in 1 day.

12 × 36 men = 18 × 60 women = 2 men = 5 women

Now, 8 men + 20 women= (4 x 5 + 20)

= (4 × 5 + 20) women = 40 women

∴ 18 women complete the work in 60 days.

∴ 40 women’ 20 days’ work

= (40 × 20)/(18 × 60) = 20/27

∴ Remaining work= 1 – 20/27 = 7/27

∴ 18 × 60 women do 1 work in 1 day.

∴ 1 women does

= 1/18 × 60 work in 1 day

∴ 1 women does in 4 days

= 4/(18 × 60) = 1/(18 × 15) work

∴ 1/(18 × 15) work is done in 4 days by 1 woman

∴ 1/27 work is done in 4 days by

= (18 × 15 × 7)/27 = 70 days women

or

Work done by 1 man in 1 day

= 1/(12 × 36)

Work done by 8 men in 20 dyas

= (8 × 20)/(12 × 36)

Again, work done by 1 women in 1 days

= 1 /(18 × 60)

Work done by 20 women in20 days = (20 × 20)/(18 ×60)

Total work done in 20 days

= (8 × 20)/(12 × 36) + (20 × 20)/(18 × 60) = 20/27

Remaining work= 7/27 = (1 – 20/27)

Now, work done by 1 women in 4 days = 4/(18 × 60)

∴ 7/27 work is done by(18 × 60 × 7)/(4 × 27) = 70 women

**2.(2)**

Clearly,

9 × 360 children = 18 × 72 men= 12 × 162 women

= 45 children = 18 men

= 27 women

= 5 children = 2 men = 3 women

Now, 4 men + 12 women + 10 children

= 4 men + 8 men + 4 men

= 16 men

∴ 18 men can complete the work in 72 days.

∴ 16 men can complete work in

= (18 × 72)/16 = 81 days

**3.(2)**

∴ 56 men can complete 1 work in 24 days

∴ 1 man complete the work in 24 × 56 days

∴ 42 men will do the some work in

= (24 × 56)/42 = 32 days

Method 2:

[Quicker Method]

∴ M1D1= = M2D2

∴ (56 × 24)/42 = 32 days

**4.(1)**

Days Women

∴ 21 : 18 : : 42 : x

x = 42 × 18/21 = 36

**5.(4)**

40 Days Men

16 30

20 x

∴ 20 : 16 : : 30 : x

= 20 × x = 16 × 30

= x = 30 × 16/20 = 24

**6.(1)**

As per given information,

8 × 4 men = 12 × 4 women= 8 × 8 children

= 32 men = 48 women= children

= 2 men = 3 women = 4 children

∴ 2 men + 8 children + 3 women

= ( 3 + 6 + 3) women = 12 women

12 women’s 2 day’s work = ½

Remaining work=1/2

∴ Required number of women = 12

**7.(4)**

Days Children

12 18

8 x

∴ 8 : 12 = 18 : x

= 8x = 12 × 18

∴ x = 12 × 18/8 = 27

Note : You can use the formula:

M1D1 = M2D2 and solved it.

**8.(1)**

According to the question.

1 man = 2 women

∴ 8 men + 4 women

= (16 + 4) women = 20 women

4 men + 8 women= 16 women

20 women’s 2 days work= 2/6 = 1/3

Remaining work = 1 – 1/3 = 2/3

∴ 20 women complete 1 work in 6 days.

∴ 16 women will do 2/3 work in

= (20 × 6)/16 × (2/3) = 5 days

**9.(2)**

(B + C)’s 1 day’s work = 1/8 ………. (i)

(A + B)’s 1 day’s work = 1/12 ………… (ii)

(A + B)’s 1 day’s work = 1/16 ……….. (iii)

On adding all these tree equations.

2 ( A + B + C)’s 1 day’s work

=1/8 + 1/12 + 1/16 = (6 + 4 + 3)/48 = 13/48

= (A +B + C)’s 1 days’ work

= 13/96

∴ A, B, and C together can complete the work in 96/13 days

**10.(5)**

10 men complete the work in 1 days.

∴ 80 men will complete the work in 1 day.

Again,

20 women complete the work in 6 days.

∴ 120 women complete the work in 1 day.

= 80 men = 120 women

= 2 men = 3 women

∴ 16 men + 18 women + 16 men+ 18 × 2/3 men = 28 men

∴ 10 men can do the work in8 days

∴ 28 men can do the work in (10 × 8)/28 = 20/7 days