X and Y together can complete a piece of work in 20 days, while Y and Z together can complete it in 24 days. After X worked on it for 10 days and Y for 18 days, Z alone completed the remaining work in another 13 days. X and Z together complete 75% of the original in:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 10 days.
Total work = LCM of 20 and 24 = 120
Efficiencies: X + Y = 120/20 = 6 and Y + Z = 120/24 = 5
So, X = 6 - Y and Z = 5 - Y
Work done: 10X + 18Y + 13Z = 120
⇒ 10(6 - Y) + 18Y + 13(5 - Y) = 120
⇒ 60 - 10Y + 18Y + 65 - 13Y = 120
⇒ Y = 1
Efficiencies: X = 6 - 1 = 5 and Z = 5 - 1 = 4
Time to complete 75% work = (0.75 × 120)/9 = 10 days