Correct Answer - Option 4 : 12, 20
Given:
X women can finish a work in 2Y days
1.5X men can finish a work in Y days
3X children can finish a work in 2Y days
8 Men, 8 Women and 8 children can finish work in 45/2 days
9 men can finish the same in Y + 20 days
Calculation:
X women can finish a work in 2Y days
It means 1 woman can complete the same work in 2XY days
⇒ 1-day work of 1 woman is 1/ (2XY) units
1.5X men can finish a work in Y days
It means 1 man can complete the same work in 1.5XY days
⇒ 1-day work of 1 man is 1/ (1.5XY) units
3X children can finish a work in 2Y days
It means 1 child can complete the same work in 6XY days
⇒ 1-day work of 1 child is 1/ (6XY) units
As we have got two relations based on men we can consider data given for men
1.5X men can finish a work in Y days
9 men can finish the same in Y + 20 days
And total work is same in both cases
So,
1.5XY = 9(Y + 20) ---(i)
Now consider
8 Men, 8 Women and 8 children can finish a work in 45/2 days
⇒ 8{(1/1.5XY) + (1/2XY) + (1/6XY)} = 1/(45/2)
⇒ 8{(2/3XY) + (1/2XY) + (1/6XY)} = 2/45
Let’s take 1/XY common
⇒ 8/XY {2/3 + 1/2 + 1/6} = 2/45
⇒ 8/XY {(4 + 3 + 1)/6} = 2/45
⇒ 8/XY {8/6} = 2/45
⇒ 64/6XY = 2/45
⇒ XY = 240
Now let’s substitute value of XY in (i)
1.5XY = 9 (Y + 20)
⇒ 1.5 (240) = 9Y + 180
⇒ 360 = 9Y + 180
⇒ 9Y = 180
⇒ Y = 20
Then, X = 12 {from (i)}
∴ values of X and Y are 12 and 20 respectively.
