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L alone can complete a work in 200 hours. M alone can complete the same work in 150 hours. L, M and N together can complete the same work in 60 hours. In how many hours can N alone complete the work?

L alone can complete a work in 200 hours. M alone can complete the same work in 150 hours. L, M and N together can complete the same work in 60 hours. In how many hours can N alone complete the work? Correct Answer 200

Let efficiencies of L, M and N be l, m and n respectively.

One-day efficiency of L : l = 1/200

One-day efficiency of M : m = 1/150

Combined one-day efficiency : l + m + n = 1/60

Substituting values of l and m, we get

1/200 + 1/150 + 1/n = 1/60

1/n = 1/60 - 1/150 - 1/200 = (10 - 4 - 3)/600 = 3/600 = 1/200

∴ N can do the work in 200 hours.

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