Question

2 men and 5 women can do a piece of work in 4 days, while one man and one woman can finish it in 12 days. How long would it take for 1 man to do the work?

Answer 1

let
Man=x & Woman=y
Then,
2x + 5y = 1/4
x + y = 1/12
or y= 1/12-x
Now
2x + 5(1/12-x)=1/4
2x+ 5/12-5x=1/4
-3x=1/4-5/12
-3x=(3-5)/12
-3x= -3/12
x=1/12
Therefore one man can finish that work in 12 days.

Answer 2

Given :

2 men and  5 women can do a piece of work in 4 days, while one man and

one woman can finish it in 12 days.

To Find :

Time taken by 1 man to do the same work.

Solution :

Let x represents man and y represents woman.

$2x+5y=4days......(1)$

$1x+1y=12days$

$5x+5y=\frac{12}{5}days=2.4days.......(2)$

By subtracting equation (1) from equation (2)

$3x=\frac{2.4\times4}{4-2.4}$

$3x=\frac{9.6}{1.6}$

$3x=6$

Since 3 men can do the same work in 6 days.

Therefore, 1 man can do  = 6 × 3 = 18 days

1 man can do the same work in 18 days.