Question

A can do a piece of work in 12 hours, B and C can do it 3 hours whereas A and C can do it in 6 hours. How long will B alone take to do the same work?

Answer 1

Time taken by A to complete the work = 12 hrs.

∴ A’s 1 hr work = 1/12…………(1)

(B + C) complete the work in 3 hrs.

∴ (B + C)’s 1 hour work = 1/3…………(2)
(1) + (2) ⇒

∴ (A + B + C)’s 1 hour work = 1/12 + 1/3 = (1+4)/12 = 5/12

Now (A + C) complete the work in 6 hrs.

∴(A + C)’s 1 hour work = 1/6

∴ B’s 1 hour work = (A + B + C)’s 1 hour work – (A + C)’s 1 hour work

= 5/12 – 1/6 = (5−2)/12 = 3/12 = 1/4

∴ B alone take 4 days to complete the work.