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I came across the following question:

If 3 boys can paint a fence in 2 days what part of the job can be completed by two boys in 1 day?

The answer to this problem is $\frac13$.

I can't manage to tackle this problem. Could anyone tell me what would be the quickest way to solve this problem (This question is a standardized test based question). Any help would be appreciated.

3 Answers 3

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Three boys paint it in two days. That means that it takes six times the amount of work a single boy can do in a day to finish painting (assuming every boy paints the same amount, of course); so one boy will take three times as long as three boys: six days. So in one day, a single boy can paint $\frac{1}{6}$th of the fence. Two boys will paint twice as much, that is $\frac{2}{6} = \frac{1}{3}$ of the fence.

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    @Rajeshwar: If it takes you six days to paint the whole fence, then how much fence are you painting each day?2012-06-01
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Ask yourself how much of the fence one boy can paint in one day. Then two boys will be able to paint twice as much.

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    @Rajeshwar: Exactly: if you can figure out *why* it takes 2 boys three days to complete the fence, then you can say why they can only paint $\frac{1}{3}$ of the fence in one day. Or were you basing your assertion on the *assumption* that the answer was correct? The point is to deduce the answer, not to use it as part of your method to find it.2012-06-01
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Imagine that the fence comprises 12 portions. In one day 6 portions will be completed by 3 boys. Meaning that 1 boy paints 2 portions. 2 boys will paint 4 portions. We need to calculate the part of job completed by 2 boys in one day I.e 4/12 =1/3