Model 4 Working with Man, Woman, Child Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on time & work topic of quantitative aptitude
(a) 6
(b) 49
(c) 7
(d) 42
The correct answers to the above question in:
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
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Read more working with man woman child Based Quantitative Aptitude Questions and Answers
Question : 1
6 men and 8 women can do a work in 10 days, Then 3 men and 4 women can do the same work in
a) 12 days
b) 24 days
c) 20 days
d) 18 days
Answer »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
Question : 2
If 16 men or 20 women can do a piece of work in 25 days. In what time will 28 men and 15 women do it?
a) 18$3/4$ days
b) 14$2/7$ days
c) 33$1/3$ days
d) 10 days
Answer »Answer: (d)
16 men = 20 women ⇒ 4 men = 5 women.
Now, according to question,
16 men complete the work in 25 days.
1 man one day’s work = $1/{25 × 16}$
4 men one day’s work = $4/{25 × 16} = 1/100$
Similarly,
1 woman one day’s work =$1/{25 × 20}$
5 women one day’s work = $5/{25 × 20} = 1/100$
28 men = $28/4$ × 5 = 35 women
[28 men + 15 women]
50 women one day’s work men= $50/{25 × 20} = 1/10$
Therefore, 28 men and 15 women can complete the whole work in 10 days.
Using Rule 12,
A = 16, B = 20, a = 25, $A_1$ = 28, $B_1$ = 15
Time taken = ${a(A × B)}/{A_1B + B_1A}$
= ${25(16 × 20)}/{28 × 20 + 15 × 16}$
= ${25 × 320}/{560 + 240}$
= ${25 × 320}/800$ = 10 days
Question : 3
One man or two women or three boys can do a piece of work in 88 days. One man, one woman and one boy will do it in
a) 48 days
b) 44 days
c) 24 days
d) 20 days
Answer »Answer: (a)
1 man ≡ 2 women ≡ 3 boys
1 man + 1 woman + 1 boy
= $(3 + 3/2 + 1)$ boys
= $({6 + 3 + 2}/2)$ boys= $11/2$ boys
$M_1D_1 = M_2D_2$
3 × 88 = $11/2 × D_2$
$D_2 = {3 × 2 × 88}/11$ = 48 days
Using Rule 13,
Here, A = 1, B = 2, C = 3, a= 88
$A_1 = 1, B_1 = 1, C_1$ = 1
Required time = $a/{A_1/A + B_1/B + C_1/C}$
= $88/{1/1 + 1/2 + 1/3} = 88/{{6 + 3 + 2}/6}$ = 48 days
Question : 4
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it ?
a) 40 days
b) 50 days
c) 45 days
d) 35 days
Answer »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
Question : 5
One man and one woman together can complete a piece of work in 8 days. A man alone can complete the work in 10 days. In how many days can one woman alone complete the work ?
a) 40 days
b) $140/9$ days
c) 30 days
d) 42 days
Answer »Answer: (a)
Work done by 1 woman in 1 day
= $1/8 - 1/10 = {5 - 4}/40 = 1/40$
One woman will complete the work in 40 days.
Using Rule 4If A alone can do a certain work in 'x' days and A and B together can do the same work in 'y' days, then B alone can do the same work in $({xy}/{x - y})$ days.
Here, x = 10 and y = 8
Woman can do work in = $({xy}/{x - y})$ days
= $({10 × 8}/{10 - 8})$ = 40 days
Question : 6
3 men and 5 women can do a work in 14 days while 5 men can do it in 14 days. 5 men and 5 women can complete the work in
a) 10 days
b) 13 days
c) 11 days
d) 12 days
Answer »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.
time & work Shortcuts and Techniques with Examples
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Model 1 Basics on Time & Work
Defination & Shortcuts … -
Model 2 Formula method ‘M1D1W1 = M2D2W2’
Defination & Shortcuts … -
Model 3 Man leaves & joins
Defination & Shortcuts … -
Model 4 Working with Man, Woman, Child
Defination & Shortcuts … -
Model 5 Split & Fraction of work
Defination & Shortcuts … -
Model 6 Efficiency of the worker
Defination & Shortcuts … -
Model 7 Working with individual wages
Defination & Shortcuts …
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