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by karthikpandian19 » Mon Dec 05, 2011 9:40 pm
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) 403.
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by Anurag@Gurome » Mon Dec 05, 2011 9:42 pm
karthikpandian19 wrote: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) 403.
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

The correct answer is C.
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