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

Answer: (a)

40 men ≡ 60 women ≡ 80 children

10 men ≡ $80/40 × 10$ = 20 children

10 women ≡ $80/60 × 10 = 40/3$ children

10 men + 10 women + 10 children

= $(20 + 40/3 +10)$ children

= $({60 + 40 + 30}/3)$ children = $130/3$ children

${M_1D_1}/W_1 = {M_2D_2}/W_2$

$D_2 = {80 × 6 × 13}/130 = 144/13$ months

Half of the work can do

= $144/13 × 1/2 = 72/13 = 5{7}/13$ months

Here, A = 40, B= 60, C = 80, a = 6

$A_1 = 10, B_1 = 10, C_1$ = 10

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

= $6/{10/40 + 10/60 + 10/80}$

= $6/{1/4 + 1/6 + 1/8}$

= $6/{{6 + 4 + 3}/24} = 144/13$

Half of the work they do in = $1/2 × 144/13$ months

= $72/13 = 5{7}/13$ months

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: (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

Answer: (a)

According to the question 5 men = 8 women

2 men = $8/5 × 2 = 16/5$ women

Total women = $16/5 + 4 = 36/5$ women

No. of days to do the same work

= ${8 × 12}/{36/5} = {8 × 12 × 5}/36$

= $40/3 = 13{1}/3$ days

Using Rule 12,

Here, A = 5, B = 8, a = 12, $A_1$ = 2 and $B_1$ = 4

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

= ${12(5 × 8)}/{2 × 8 + 4 × 5}$

= ${12 × 40}/36 = 33{1}/3$ days