Time and Work
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Q.

Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How many days will a woman take to do the job, if she works alone on it?

 A.

18

 B.

36

 C.

54

 D.

None

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Solution:
Option(C) is correct

Let the amount of work done by a man in a day be $‘m’$ and the amount of work done by a woman in a day be $‘w’$.

Therefore, 4 men and 3 women will do $4m+3w$ amount of work in a day. If 4 men and 3 women complete the entire work in 6 days, they will complete \(\left(\dfrac{1}{6}\right)^{th}\)of the work in a day.

Hence, \(4m+3w=\dfrac{1}{6}\).......(1)

and from statement (2), \(5m+6w=\dfrac{1}{4}\)......(2)

Solving eqn (1) and eqn (2), we get \(3m=\dfrac{1}{12}\) or \(m=\dfrac{1}{36}\)  i.e. a man does \(\left(\dfrac{1}{36}\right)^{th}\) of the work in a day. Hence he will take 36 days to do the work.

Substituting the value of $m$ in eqn (1), we get \(4\times \dfrac{1}{36}+3w=\dfrac{1}{6}\)

\(3w=\dfrac{1}{6}-\dfrac{1}{9}=\dfrac{1}{18}\)

\(w=\dfrac{1}{54}\)

i.e. a woman does \(\left(\dfrac{1}{54}\right)^{th}\) of the work in a day. Hence she will take 54 days to do the entire work.

Alternate Method:

As suggested by Abhishek Fauzdar an alternative calculation is shown below:

From the question,

$\Rightarrow (4 \text{ men} + 3 \text{ women}) \times 6\text{ days} $ $= (5 \text{ men}$ $+ 6\text{ women}) \times 4 \text{ days}$.

$\Rightarrow 24 \text{ man days} $ $+ 18 \text{ woman days} $ $ = 20 \text{ man days} $ $+ 24 \text{ woman days} $

$\Rightarrow 4 \text{man days} $ $= 6 \text{women days}$

$\Rightarrow$ total work,

$=24 \text{ man days} $ $+ 18 \text{ woman days}$

$=24\times \left(\dfrac{6}{4}\right) \text{ woman days} $ $+18 \text{ woman days}$

$=36 \text{ woman days} $ $+18 \text{ woman days}$

$= \textbf{54 women days}$


(5) Comment(s)


Deeksha Verma
 ()

As 4 men and 3 women can complete a work in 6 days

4/M+3/W=1/6----(eq1)

As 5 men and 6 women can complete a work in 4 days

5/M+6/W=1/4----(eq2)

Solve both the equations.

1/W=1/54

=>w=54



Bighneswar Behera
 ()

4m+3w=6 5m+6w=4

24m+18w=20m+24w

4m=6w

3m=2w

(4*3)+(3*2)=6

12+6=6

18*6=108(t.w)

1 woman 108/2=54



SONIA
 ()

4M + 3W = 1/6........(1) * 5

5M + 6W = 1/4........(2) * 4

---------------------------------

20M + 15 W = 5/6

20M + 24 W = 1

CANCELLED FIRST EQUATION 24-15 = 9 W

9W = 1-5/6

9W = 1/6

W = 1/54



Tarna
 ()

4m+3w=6days

1 day work -> 4m+3w=1/6

5m+6w=4days

1 day work -> 5m+6w=1/4

now

5*(4m+3w=1/6)............(1)

4*(5m+6w=1/4)............(2)

after solving (1) and (2) we get

9w=1/6

1w =1/54 work

that's mean 1 woman can complete 2ork in 54 days.



Abhishek Fauzdar
 ()

$4\times 6\text{ man-days} $$+ 3 \times 6 \text{ women−days} $$= 4\times 5 \text{ man−days} $$+ 4 \times 6 \text{ women-days}$.

$\Rightarrow 4 \text{man-days} = 6 \text{women-days}$

therefore, total work =>36 women-days +18 women- days =54 women days