Concept of “Time and Work” [समय और काम]-05

Question:  A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. In how many days can all of A, B and C together finish the whole work? [Ans. (b) 10 days]

(a)  20 days  (b) 10 days  (c) 5 days  (d) 12 days  (e) None of these

Solution: 

Detailed Solution: Given that A + B can do a work in 12 days; B + C can do it in 15 days and C + A can do the same work in 20 days.

First Method: (A + B), (B + C) and (C + A) can do the same work in 1/[1/x+1/y+1/z] days

So, 2 (A + B + C) can do the work in1/[1/12 +1/15 +1/20] days = 60/[5+4+3] days = 60/12 days = 5 days. 

Therefore, (A + B + C) can finish the whole work in 5×2 = 10 days. Ans.

Second Method: (A + B), (B + C) and (C + A) can do the same work in xyz/[xy + yz + zx] days

So, 2 (A + B + C) can do a work in [12 × 15 × 20]/[12×15 + 15×20 +20 ×12] = 5 days

Therefore, (A + B + C) can finish the whole work in 5×2 = 10 days. Ans.