Question

A and B complete a piece of work in 24 days. B and C do the same work in 36 days; and A, B, and C together finish it in 18 days. In how many days will:
(i) A alone,
(ii) C alone,
(iii) A and C together, complete the work?

Answer 1

A and B complete a piece of work in = 24 days

B and C complete a piece of work in = 36 days

(A+B+C) complete a piece of work in = 18 days

(A+B)’s 1-day work = `1/24`

(B+C)’s 1-day work = `1/36`

(A+B+C)’s 1-day work = `1/18`

(i) A's 1-day work =`1/18-1/36`

`=(2-1)/36=1/36`

∴ A will complete the work in = 36 days

(ii) C's 1-day work =`1/18-1/24`

`=(4-3)/72=1/72`

∴ C will complete the work in = 72 days

(iii) (A+C)'s 1-day work =`1/36+1/72`

`=(2+1)/72=3/72`

`=1/24`

∴ (A+C) will complete the work in = 24 days