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Question

# A certain fraction is equivalent to 12. If 3 is added to its numerator and 2 is added to its denominator, the resulting fraction is equivalent to 34. What is the numerator of the original fraction?

A
2
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B
3
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C
4
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D
5
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E
6
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Solution

## The correct option is B 3Let the fraction be xy which is equivalent to 12.So, we get 2x=y.Now 3 is added to numerator and 2 is added to denominator. We get (x+3)(y+2) =34.∴4x+12=3y+6∴4x+6=3ySubstitute 2x=y in the equation,2y+6=3y⇒y=6Now, x=y2=62=3Therefore, the numerator of original fraction is x=3.

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