X and Y can complete a work in 5 days. Y and Z can complete the same work in 6 days. Z and X can complete the same work in 15/2 days. In how many days will X, Y and Z together complete the work?
1). 2
2). 4
3). 3
4). 2/5
Time taken by X + Y to complete a work = 5 days
Time taken by Y + Z to complete a work = 6 days
Time taken by Z + X to complete a work = 15/2 days
Total work = LCM of (5, 6 and 15/2) = 30 units
Efficiency of X + Y together = 30/5 = 6 units/day
Efficiency of Y + Z together = 30/6 = 5 units/day
Efficiency of Z + X together = 30/(15/2) = 4 units/day
Efficiency of X + Y + Z together = 2(X + Y + Z) = 6 + 5 + 4 = 15 units/day
X + Y + Z = 15/2 = 7.5 units/day
∴ Total time taken by X + Y + Z together to complete the work = 30/7.5 = 4 days