X can complete 1/4 of a work in 3 days and Y can complete 1/6 of the same work in 4 days, X and Y worked together for 6 days and Z alone completed the remaining work in 8 days. If Y and Z work together, how much time will they take to complete the same work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 13(5/7) days.
Given:
X can complete 1/4 of a work in 3 days
Y can complete 1/6 of the same work in 4 days,
X and Y worked together for 6 days and Z alone completed the remaining work in 8 days
Formula used:
Total work = Efficiency × time ---- (1)
Calculation:
X can complete 1/4 of a work in 3 days
X can complete the whole work in 12 days
Y can complete 1/6 of the same work in 4 days
Y can complete the whole work in 24 days
Total work (LCM of 12 and 24) = 24 units
Efficiency of X = 24/12 = 2 units
Efficiency of Y = 24/24 = 1 unit
X and Y worked together for 6 days = (2 + 1) × 6 = 18 units
Remaining work = 24 - 18 = 6 units
Z alone completed the remaining work in 8 days
Efficiency of Z = 6/8 = 3/4 units
Efficiency of Y and Z = 1 + 3/4 = 7/4
Required time taken = 24/(7/4) = 96/7 or 13(5/7) days