Question

X and Y together can do a work in \(2 \frac{2}{5}\) days, Y and Z together can do the same work in 3 days, and X and Z together can do the same work in 4 days. The time taken by X, Y and Z together to do the same work is: 
1. \(\frac{1}{2}\) day
2. 1 day
3. 2 days
4. \(2 \frac{1}{2}\)

Answer 1

Correct Answer - Option 3 : 2 days

Given:

(X + Y)'s 1 day's work = 5/12

Calculation:

Let X's, Y's and Z's 1 day's work be 1/X, 1/Y and 1/Z respectively.

⇒ 1/X + 1/Y = 5/12

⇒ 1/Y + 1/Z) = 1/3

⇒ (1/X + 1/Z) = 1/4

Then,

2/X + 2/Y + 2/Z = 5/12 + 1/3 + 1/4

1/X + 1/Y + 1/Z = 1/2

∴ Work will be completed in 2 days when X, Y and Z will work together.