X, Y, and Z can work complete a piece of work in 46 days, 92 days, and 23 days, respectively. X started the work. Y joined him after 7 days. If Z joined them after 8 days from the beginning, then for how many days did Y work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 11
Days in which X can complete the work = 46 days
Days in which Y can complete the work = 92 days
Days in which Z can complete the work = 23 days
Days after which Y joined = 7 days
Days after which Z joined = 8 days
Efficiency = Total work/Time taken to complete work individually
Total work = LCM of 23, 46, 92 = 92 units
Efficiency of X = 92/46 = 2 units/day
The efficiency of Y = 92/92 = 1 unit/day
The efficiency of Z = 92/23 = 4 units/day
Work done in 7 days by X working alone = 2 units × 7 = 14 units
Work done by X and Y on 8th day = (2 + 1) × 1 = 3 units
Total work done until 8th day = 14 + 3 = 17 units
Remaining work = 92 - 17 = 75 units
Work done by X , Y and Z in one day = 2 + 1 + 4 = 7 units
Total time taken = 75/7 days
Total days worked by Y = (75/7) + 1 = 82/7 = 11 5/7p days