# | | 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

**Answer:** **(B)** **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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