Model 4  Working with Man, Woman, Child Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Let 1 man’s 1 day’s work = x and

1 woman’s 1 day’s work = y

Then, 4x + 6y = $1/8$ and

$3x + 7y = 1/10$

From both equations,

we get y = $1/400$

10 women’s 1 day’s work = $10/400 = 1/40$

10 women will finish the work in 40 days.

Using Rule 11,

$A_1 = 4, B_1 = 6, D_1$ = 8

$A_2 = 3, B_2 = 7, D_2$ = 10

$A_3 = 0, B_3$ = 10

Required time = ${D_1D_2(A_1B_2 - A_2B_1)}/{D_1(A_1B_3 - A_3B_1) - D_2(A_2B_3 - A_3 B_2)}$

= ${8 × 10(4 × 7 - 3 × 6)}/{8(4 × 10 - 0 × 6) - 10(3 × 10 - 0 × 7)}$

= ${80 × 10}/20$ = 40 days

Answer: (b)

Using Rule 11,

According to the question,

1 man ≡ 2 women ≡ 4 boys

1 man + 1 woman + 1 boy

= (4 + 2 +1) boys = 7 boys

$M_1D_1 = M_2D_2$

7 × 7 = 1 × $D_2$

∴ $D_2$ = 49 days

Answer: (c)

6m + 8w ≡ 10 days

2 (3m + 4w) ≡ 10 days

3m + 4w ≡ 20 days

[Since the workforce has become half of the original force, so number of days must be double].

Using Rule 14,

Let us assume efficiency of 6 men = efficiency of 8 men.

A = 6, a = 20, B = 8, b = 20

$A_1 = 3, B_1$ = 4

Required time = $1/{A_1/{A × a} + B_1/{B × b}}$

= $1/{3/{6 × 20} + 4/{8 × 20}}$

= $1/{1/40 + 1/40} = 40/2$ = 20 days

Answer: (a)

5 men can do 1 work in 14 days.

3 men will do $3/5$ work in 14 days.

Remaining work = $1 - 3/5 = 2/5$

5 women do $2/5$ work in 14 days.

Time taken by 5 women in doing 1 work

= ${14 × 5}/2 = 35$ days

(5 men + 5 women)’s 1 day’s work

= $1/14 + 1/35 = {5 + 2}/70 = 7/70 = 1/10$

∴Required time = 10 days.

Answer: (b)

12 (3 men + 4 boys) = 10 (4 men + 3 boys)

36 men + 48 boys = 40 men + 30 boys

4 men = 18 boys or 2 men = 9 boys

4 men + 3 boys

= 21 boys who do the work in 10 days

and, 2 men + 3 boys = 12 boys

$M_1D_1 = M_2D_2$

21 × 10 = 12 × $D_2$

$D_2 = {21 × 10}/12 = 35/2 = 17{1}/2$ days

Using Rule 11,

Here, $A_1 = 3, B_1 = 4, D_1 = 12$

$A_2 = 4, B_2 = 3, D_2$ = 10

$A_3 = 2, B_3$ = 3

Required time = ${D_1D_2(A_1B_2 - A_2B_1)}/{D_1(A_1B_3 - A_3B_1) - D_2(A_2B_3 - A_3 B_2)}$ days

= ${12 × 10(3 × 3 - 4 × 4)}/{12(3 × 3 - 2 × 4) - 10(4 × 3 - 2 × 3)}$

= ${-120 × 7}/{12 - 60} = {-840}/{-48} = 70/4$

= $35/2 = 17{1}/2$ days

Answer: (c)

20 women complete 1 work in 16 days.

16 men complete same work in 15 days

16 × 15 men ≡ 20 × 16 women

3 men ≡ 4 women

∴ Required ratio = 4 : 3