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? A. 18 days B. 24 days C. 30 days D. 36 days

Given, 

Time taken by A and B to do the work = 30 days

A and B one day work = 1/30

Time taken by B and C to do the work = 24 days

B and C one day work = 1/24

Time taken by C and A to do the work = 20 days

C and A one day work = 1/20

Therefore, one day work of A, B and C= 1/2 [1/30 + 1/24 + 1/20] 

= 1/16

Ten days work of A, B and C = 10/16 = 5/8

Remaining work is done by A = 1 – 5/8 = 3/8

A’s one day work = 1/16 – 1/24 = 1/48

Thus, 3/8 work done by A alone = 3/8 x 48 = 18 days

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