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A and B working together can do a piece of work in 24 days, B and C working together can do the same piece of work in 15 days and A and C working toge
Question



A and B working together can do a piece of work in 24 days, B and C working together can do the same piece of work in 15 days and A and C working together can do the same piece of work in 20 days. They all worked together for 6 days and then A and C leaves the work, then in how many days will B take to finish the remaining work?

A.

15 days

B.

8 days

C.

12 days

D.

21 days

E.

18 days

Correct option is E


Let the total work be 120 unit (LCM of 24, 15 and 20)
So, the efficiency of A + B = 5 unit/day
The efficiency of B + C = 8 unit/day
The efficiency of A + C = 6 unit/day
The efficiency of A + B + C = (5+8+6)/2 = 19/2 unit/day
So, the efficiency of B =19/2 -6 = 7/2 unit/day
Let the time taken by B to complete the remaining work be x days.
ATQ,

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