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A and B can do a piece of work in 30 days , while B and C can do the same work in 24 days and C and A in 20 days . They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

18 days
24 days
30 days
36 days

Correct Answer: 18 days

Explanation:

2(A+B+C)'s 1 day work = 1/30 + 1/24 + 1/20 = 1/8

=>(A+B+C)'s 1 day's work= 1/16

work done by A,B and C in 10 days=10/16 = 5/8

Remaining work= 3/8

A's 1 day's work= $\frac{1}{16} - \frac{1}{24} = \frac{1}{48}$

Now, 1/48 work is done by A in 1 day.

So, 3/8 work wil be done by A in =48 x (3/8) = 18 days

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