# | | Question 5

A, B and C can do a piece of work in 10, 12 and 15 days respectively.They all start the work together but A leaves after the 2 days of work and B leaves 3 days before the work is completed.Find the number of days the work completed.
(A) 4 days
(B) 7 days
(C) 6 days
(D) 9 days

Explanation: Total work done is LCM(10, 12, 15)=60 unit
A’s efficiency = 60/10= 6
B’s efficiency = 60/12= 5
C’s efficiency = 60/15= 4
First two days all work together
So, the work completed in first two days= 15 x 2 = 30 unit
Remaining work= 60 – 30 = 30 unit
If B completes 3 day work also = 3 x 5 = 15 unit
Total work remaining= 30 + 15 = 45 unit
Number of days B and C works= 45/9=5

Total number of days to complete the work = 2 + 5 = 7 days.

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