Q) 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) 6 days                     b) 10 days             c) 15 days                     d) 20 days

Ans:

(A + B)’s 1 day work = 1/30

(B + C)’s 1 day’s work = 1/24

(A + C)’s 1 day’s work = 1/20

By adding all the above 3 equations, we get:

(A + B)’s 1 day work + (B + C)’s 1 day’s work + (B + C)’s 1 day’s work

= 1/30 + 1/24 + 1/20 = 15/120 = 1/8

∴ 2 x (A + B + C)’s 1 day’s work = 1/8

∴ (A + B + C)’s 1 day’s work = 1/16

∴ (A + B + C)’s 10 days’ work = 10/16 = 5/8

∴ Balance work = 1 – 5/8 = 3/8

A’s 1 day work = (A + B + C)’s 1 day work – (B + C)’s 1 day work = 1/16 – 1/24 = 1/48

Since time taken by A to do 1/48 work = 1 day

∴ Time taken by A to do 3/8 work = (3/8)/(1/48) = 18 days

Hence, Answer is [A].

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