Correct Answer - Option 3 : 100
Given:
X and Y finish a work in 50 days.
They work for 20 days and then Y left.
X finished the remaining work in 60 days.
Formula Used:
If A and B can together finish a work in t days and alone can finish the work in a and b days respectively,
Then, 1/a + 1/b = 1/t
Work = Time × Efficiency
Calculation:
Total work = LCM of 50, 60 = 300 units
Efficiency of x and y = 300/50 = 6
Amount of work done in 20 days = (6 × 20) units = 120 units
Remaining work = (300 – 120) units = 180 units
X can finish 180 units of work in 60 days.
Efficiency of x = 180/60 = 3
Combined efficiency of x + y = 6
So, the time y will take to finish the work = 300/3 = 100 days
∴ y will take 100 days to finish the work.
