Question

A and B together can do a piece of work in 10 days, B and C can do the same work together in 12 days, A and C can do together in 15 days. How long will it take to complete the work working three of them altogether?

Answer 1

(A + B)’s 1 day’s work = 1/10……….(1)

(B + C)’s 1 day’s work = 1/12……….(2)

(A + C)’s 1 day’s work = 1/15……….(3)

(l) + (2) + (3) ⇒

[A + B + B + C + A + C]’s 1 day work

= 1/10 + 1/12 + 1/15

(2A + 2B + 2C)’s 1 day work = (6+5+4)/60

2(A + B + C)’s 1 day work = 15/60

(A + B + C)’s 1 day’s work = 1/(4×2) = 1/8

∴ A + B + C work together to finish the work in 8 days.