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

Answer: (c)

2 × 10 men + 3 × 10 women = 3 × 8 men + 2 × 8 women

20 men + 30 women = 24 men + 16 women

4 men = 14 women or 2 men = 7 women

2 men + 3 women = 10 women

2 men + 1 woman = 8 women

$M_1D_1 = M_2D_2$

10 × 10 = 8 × $D_2$

$D_2 = 25/2 = 12{1}/2$ days

Using Rule 11

Here, $A_1 = 2, B_1 = 3, D_1$ = 10

$A_2 = 3, B_2 = 2, D_2$ = 8

$A_3 = 2, B_3$ = 1

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.

= ${10 × 8(2 × 2 - 3 × 3)}/{10(2 × 1 - 2 × 3) - 8(3 × 1 - 2 × 2)}$

= ${80(4 - 9)}/{10(2 - 6) - 8(3 - 4)}$

= ${-400}/{-40 + 8} = {-400}/{-32} = 25/2 = 12{1}/2$ days

Answer: (a)

1 man = 2 women ≡ 3 boys 1 man + 1 woman + 1 boy

= $(3 + 3/2 + 1)$ boys = $11/2$ boys

$M_1D_1 = M_2D_2$

$3 × 88 = 11/2 × D_2$

$D_2 = {2 × 3 × 88}/11$ = 48 days

Here, A = 1, B= 2, C = 3, a = 88

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

Time taken = $a/{A_1/A + B_1/B + C_1/C}$

= $88/{1/1 + 1/2 + 1/3}$

= ${88 × 6}/{6 + 3 + 2}$ = 48 days

Answer: (a)

6 men = 12 women ⇒ 1 man = 2 women

Now, 8 men + 16 women

= (8 × 2 + 16) women = 32 women

12 women can do a work in 20 days.

1 woman can do the work in 20 × 12 days.

32 women can do the twice work in = ${20 × 12 × 2}/32$ = 15 days.

Using Rule 12,

Here, A = 6, B= 12, a = 20, $A_1$ = 8, $B_1$ = 16

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

= ${20(6 × 12)}/{8 × 12 + 16 × 6}$

= ${20 × 72}/192 = 15/2$

They will do the twice as big work in $2 × 15/2$ days = 15 days

Answer: (b)

10 men ≡ 20 boys ⇒ 1 man ≡ 2 boys

8 men + 4 boys = (16 + 4) boys = 20 boys

Hence, 8 men and 4 boys will make 260 mats in 20 days.

Answer: (d)

10 men ≡ 20 women

1 man = 2 women = 5 children

1 woman = 2 children

5 men + 5 women + 5 children

= 20 + 10 + 5 = 35 children

$M_1D_1 = M_2D_2$

40 × 7 = 35 × $D_2$

$D_2 = {40 ×7}/35$ = 8 months

5 men, 5 women and 5 children can do half of the work in 8 months

Required time = 4 months.

Using Rule 13,

Here, A = 10, B= 20, C = 40, a = 7

$A_1 = 5, B_1 = 5, C_1$ = 5

Time taken to do same work = $a/{A_1/A + B_1/B + C_1/C}$

= $7/{5/10 + 5/20 + 5/40}$

= $7/{1/2 + 1/4 + 1/8}$

= $7/{{4 + 2 + 1}/8}$ = 8 months

Half of the work they do in 4 months.

Answer: (a)

3 men’s work = 5 women’s work

1 man’s work = $5/3$ women’s work

6 men’s work = $5/3$ × 6

=10 women’s work

6 men + 5 women = 15 women

5 women can do work in 12 days.

Hence, 15 women can do it in ${5 × 12}/15$ = 4 days

Using Rule 12,

Here, A = 3, B = 5, a = 12, $A_1$ = 6 and $B_1$ = 5

Required time = ${a(A × B)}/{A_1B + B_1A}$

= ${12(3 × 5)}/{6 × 5 + 5 × 3}$

= ${12 × 15}/45$ = 4 days