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
