**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 alone, (iii) A and C together,…**

###### Answers:

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 =

(B+C)’s 1 day work =

(A+B+C)’s 1 day work =

(i) A’s 1 day work = 1/18 – 1/36

= (2 – 1)/36 = 1/36

(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