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L alone can do a work in 100 hours. M alone can do the same in 150 hours. L, M and N together can do the same work in 30 hours. In how many hours can N alone do the work?

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L alone can do a work in 100 hours. M alone can do the same in 150 hours. L, M and N together can do the same work in 30 hours. In how many hours can N alone do the work?
1). 65
2). 60
3). 40
4). 90


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1 answers

2 vote
Answered by on | Votes 2 |

Given,

L’s 1 hour’s work = 1/100

M’s 1 hour’s work = 1/150

Let N can complete work in n days.

N’s 1 hour’s work = 1/n

Given,

(L + M + N)’s 1 hour’s work = 1/30

⇒ 1/30 = (1/100) + (1/150) + (1/n)

⇒ 1/30 = 1/60 + 1/n

⇒ 1/n = 1/30 - 1/60

⇒ 1/n = 1/60

∴ N can complete work in 60 days.

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