# Moderate Time and Work Solved QuestionAptitude Discussion

 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

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