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Question

# If the numerator is decreased by 1 and denominator is multiplied by 2, then the resulting fraction is 15.If the numerator is increased by 12 and denominator is multiplied by 6, then the resulting fraction is 12. What is the difference between the numerator and the denominator?

A
1
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B
-2
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C
3
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D
-5
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Solution

## The correct option is B -2Let the fraction be xy. Then, according to question, we have x−12y=15 and x+126y=12 On simplification, 5x−2y=5...(1) 2x−6y=−24⟹x−3y=−12...(2) From (2), x=3y−12. Substituting this value of x in (1), 5(3y−12)−2y=5⟹13y=65⟹y=5 x=3y−12=3(5)−12=3 ⟹x−y=3−5=−2

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