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Arithmetic Aptitude :: Time and Work

9. 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 ?

Answer: Option A

Explanation :

(A & B)'s 1 day work = 1/30
(B & C)'s 1 day work = 1/24
(C & A)'s 1 day work = 1/20

so 2 (A + B + C)'s 1 day's work = (1/30+1/24+1/20) = 15/120 = 1/8

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

Work done by A, B and C in 10 days = (10*1/16) = 5/8
so left work = (1?5/8)=3/8

A's 1 day's work (1/16?1/24)=1/48

=> 1/48 part of work is done by A = 1 day.

So, 3/8 part of work will be done by A = (48?3/8) = 6*3 = 18 days.

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