Question

A, B and C can complete a work in 5 days. If A and C can complete the same work in 7½ days and A alone in 15 days then, in how many days can B and G finish the work?

Answer 1

A + B + C complete the work in 5 days.

∴ (A + B + C)’s 1 day work = 1/5

(A + C) complete the work in 7 1/2 days = 15/2 days

∴ (A + C)’s 1 day work = 1/15/2 = 2/15

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

1/5 – 2/15 = 3/15 – 2/15

C’s 1 day work = (A + C)’s 1 day work – A’s 1 day work

= 2/5 – 1/15 = 1/15

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

= 1/15 + 1/15 = 2/15

∴ (B + C) can complete the work in 1/(2/15) days.

= 15/2 days = 71/2 days

∴B and C finish the work in 71/2 days.