Question

X and Y together can finish the work in 26 days. If X leaves after 10 days of working, and his place is taken up by Z, Y and Z finish the remaining work in 16 days. Find the time taken by Z to finish the work alone, if X is three times as efficient as Y.

1. 35(2/3) days
2. 34(2/3) days
3. 34(1/3) days
4. 32(1/3) days
5. 32(2/3) days

Answer 1

Correct Answer - Option 2 : 34(2/3) days

Given:

X and Y finish work together in 26 days.

X leaves after 10 days.

Y and Z finish the remaining work in 16 days.

The ratio of efficiency of X and Y = 3 ∶ 1

Concept used:

Work = Time × Efficiency

Calculation:

Total work done by X and Y = (1x + 3x) × 26 = 104x

Let the efficiency of Z be ‘z’.

Total work = (1x + 3x) × 10 + (1x + z) × 16

⇒ 104x = 40x + (1x + z) × 16

⇒ 1x + z = 4x

Or, efficiency of Z = 3x

Time is taken by Z to finish the work alone = 104x/3x = 34(2/3) days.

∴ Z will take 34(2/3) days to finish the work.