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it takes Alice and Bea 24

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it takes Alice and Bea 24

by sanju09 » Tue Sep 14, 2010 3:59 am
Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 24 hours to paint a house, then how many hours will it take Bea to paint a house alone?
(A) 28
(B) 30
(C) 32
(D) 36
(E) 40


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by kmittal82 » Tue Sep 14, 2010 4:28 am
Let time taken by Alice = 3x, then time taken by Bea = x

Let their time taken together = T

1/x + 1/3x = 1/T

=> t = 3x/4 = 24 => x = 32 = Time taken by Bea

(C) ?
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by Rahul@gurome » Tue Sep 14, 2010 4:31 am
Let Alice takes x hours to paint a house.
Then Bea takes x/3 hours to paint the house.
1 hour work of Alice = 1/x
1 hour work of Bea = 3/x
(1/x) + (3/x) = 1/24 implies x = 96 hrs, that is Alice takes 96 hrs to paint the house, which Bea could have painted in 96/3 = 32 hrs

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by ankur.agrawal » Tue Sep 14, 2010 4:34 am
Alice and Bea 24 hours to paint a house: means that in 1 hr they will complete 1/24th of the work.

Bea can paint a house three times faster than Alice can paint a house: Means that if alice takes t time to complete a work Bea will take (1/3) t to complete same work.

Alice - takes t time to complete 1 work - in 1 hr it will do - 1/t work

Bea- takes (1/3)t time to complete the same work- in 1 hr it will do- 1/(t/3) work= 3/t work

1/t+ 3/t = 1/24

Solving this we get t=96. So bea will take 1/3 *96 = 32 hrs to do the work.

So C.
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