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**A, B and C together can do a piece of work in 15 days, B alone can do it in 30 days and C alone can do it in 40 days. In how many days will A alone do the work?**

Answer:

Given:

(A + B + C) can do a piece of work in = 15 days

(A + B + C)’s 1 day work = 1/15

B alone can do a piece of work in = 30 days

B’s 1 day work = 1/30

C alone can do a piece of work in = 40 days

C’s 1 day work = 1/40

So, A’s 1 day work = (1/15) – [1/30 + 1/40]

= (1/15) – [(4+3)/120]

= (1/15) – (7/120)

= (8-7)/120

= 1/120

∴ A can do a piece of work in = 120 days.

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