Question
If the numerator of a fraction is increased by 2 and its denominator is decreased by 1, it becomes 23. If the numerator is increased by 1 and the denominator is increased by 2, it becomes 13. Find the fraction.
Answer: Option A
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A
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A
Let the fraction be xy
∴ x+2y−1=23 and x+1y+2=13
⇒ 3x−2y=−8....(i)
and 3x−y=−1......(ii)
⇒3x−2y=−8
−(3x−y=−1)
⇒3x−2y=−8
−3x+y=1
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−y=−7
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⇒y=7
Substituting y = 7 in equation (ii), we get
3x−(14)=−8
3x=−8+14=6
∴x=2
⇒x=2 and y=7
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