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Question

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction. [CBSE 2010]

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Solution

Let the fraction be xy.
As per the question
x+y=4+2xy-x=4 .....i
After changing the numerator and denominator
New numerator = x + 3
New denominator = y + 3
Therefore
x+3y+3=233x+3=2y+33x+9=2y+62y-3x=3 .....ii
Multiplying (i) by 3 and subtracting (ii), we get
3y-2y=12-3y=9
Now, putting y = 9 in (i), we get
9-x=4x=9-4=5
Hence, the fraction is 59.

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