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

Answer: (c)

5 × 6 men = 10 × 5 women

3 men = 5 women

5 women + 3 men = 6 men

5 men complete the work in 6 days

6 men will complete the work in ${5 × 6}/6$ = 5 days

Here, A = 5, a = 6, B = 10, b = 5, $A_1$ = 3, $B_1$ = 5

Time taken = $1/{A_1/{A × a} + B_1/{B × b}}$

= $1/{3/{5 × 6} + 5/{10 × 5}}$

= $1/{1/10 + 1/10}$ = 5 days

Answer: (c)

1 man ≡ 2 women ≡ 3 boys

1 man + 1 woman + 1 boy

≡ 3 boys + $3/2$ boys + 1 boy

≡ $(3 + 3/2 + 1)$ boys ≡ $11/2$ boys

By $M_1D_1 = M_2D_2$,

3 × 44 = $11/2 × D_2$

$D_2 = {2 × 3 × 44}/11$ = 24 days

Using Rule 13,

Here, A = 1, B= 2, C = 3, a = 44

$A_1 = 1, B_1 = 1, C_1$ = 1

Required time = $a/{A_1/A + B_1/B + C_1/C}$ days

= $44/{1/1 + 1/2 + 1/3} = {44 × 6}/11$ = 24 days

Answer: (b)

Part of work done by 2 men and 2 women in 2 days.

= $2(2/20 + 8/30)$

= $2(1/10 + 8/30) = 2({3 + 8}/30)$

= $22/30 = 11/15$

= Remaining work =$1 - 11/15 = 4/15$

Work done by 1 boy in 2 days

= $2/60 = 1/30$

Number of boys required to assist = $4/15 × 30 = 8$

Using Rule 14,

Here, A = 1, B = 1, C = 1

a = 20, b = 30, c = 60

$A_1 = 2, B_1$ = 8

Required time = $1/{A_1/{A × a} + B_1/{B × b} + C_1/{C × c}$

2 = ${1/{2/{1 × 20} + 8/{1 × 30} + x/{1 × 60}$

2 = $10/{2/2 + 8/3 + x/6}$

2 = $10/{{6 + 16 + x}/6}$

22 + x = 30 ⇒ x = 8

∴ Number of boys = 8

Answer: (a)

Time taken by boy = x days

$1/10 + 1/24 + 1/x = 1/6$

$1/x = 1/6 - 1/10 - 1/24$

= ${20 - 12 - 5}/120 = 3/120 = 1/40$

x = 40 days

Using Rule 18,

Here , x = 6, y = 10, z = 24

Number of days = ${xyz}/{yz –x(y + z)}$ days

= ${6 × 10 × 24}/{10 × 24 - 6(10 + 24)}$

= $1440/{240 - 204} = 1440/36$ = 40 days

Answer: (d)

1 man’s 1 day’s work = $1/3$

1 woman’s 1 day’s work = $1/4$

1 boy’s 1 day’s work = $1/12$

(1 man + 1 woman)’s $1/4$ day’s work = $1/4(1/3 + 1/4) = 7/48$

Remaining work = $1 - 7/48 = 41/48$

Now, 1 boy’s $1/4$ day’s work = $1/4 × 1/12 = 1/48$

$41/48$ work will be done by $41/48$ × 48 = 41 boys.

Answer: (d)

3 men = 4 women

1 man = $4/3$ women

7 men = ${7 × 4}/3 = 28/3$ women

7 men + 5 women = $28/3 + 5$

= ${28 + 15}/3 = 43/3$ Women

Now, $M_1D_1 = M_2D_2$

4 × 43 = $43/3 × D_2$ ,

where $D_2$ = number of days

$D_2 = {4 × 3 × 43}/43$ = 12 days.

Using Rule 12,

Here, A = 3, B = 4, a = 43, $A_1$ = 7 and $B_1$ = 5

Time taken = ${a(A × B)}/{A_1B + B_1A}$

= ${43(3 × 4)}/{7 × 4 + 5 × 3}$

= ${43 × 12}/43$ = 12 days