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) 8 days
(b) 17$1/2$ days
(c) 5$5/11$ days
(d) 22 days
The correct answers to the above question in:
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
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Read more working with man woman child Based Quantitative Aptitude Questions and Answers
Question : 1
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.
Question : 2
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 : 3
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 : 4
Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. The ratio between the capacity of a man and a woman is
a) 5 : 3
b) 3 : 4
c) 4 : 3
d) 5 : 7
Answer »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
Question : 5
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work ?
a) 12$1/2$ days
b) 8 days
c) 7 days
d) 2 days
Answer »Answer: (a)
According to the question,
20 men + 30 boys = 24 men + 16 boys
4 men = 14 boys ⇒ 2 men = 7 boys
2 men + 1 boy = 8 boys
2 men + 3 boys = 10 boys
By $M_1D_1 = M_2D_2$
10 × 10 = 8 × $D_2$
$D_2 = {10 × 10}/8 = 25/2 =12{1}/2$ 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
= ${10 × 8(2 × 2 - 3 × 3)}/{10(2 × 1 - 2 × 3) - 8(3 × 1 - 2 × 2)}$
= ${80 × -5}/{-40 + 8} = 12{1}/2$ days
Question : 6
If 8 men or 12 boys can do a piece of work in 16 days, the number of days required to complete the work by 20 men and 6 boys is
a) 8$1/3$ days
b) 5$1/3$ days
c) 6$1/3$ days
d) 7$1/3$ days
Answer »Answer: (b)
8 men ≡ 12 boys ⇒ 4 men ≡ 6 boys
20 men ≡ 30 boys
20 men + 6 boys = 36 boys
$M_1D_1 = M_2D_2$
12 × 16 = 36 × $D_2$
$D_2 = {12 × 16}/36 = 16/3 = 5{1}/3$ days
Using Rule 12,
Here, A = 8, B = 12, a = 16
$A_1 = 20, B_1$ = 6,
Required number of days = $a/{A_1/A + B_1/B} = 16/{20/8 + 6/12}$
= $16/{5/2 + 1/2} = {16 × 2}/6 = 5{1}/3$ 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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