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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 of 2: 3. Determine the fraction.
Solution
Let the required fraction be `x/y`.
As per the question
x + y = 4 + 2x
⇒ y – x = 4 ……(i)
After changing the numerator and denominator
New numerator = x + 3
New denominator = y + 3
Therefore
`(x+3)/(y+3) = 2/3`
⇒3(x + 3) = 2(y + 3)
⇒3x + 9 = 2y + 6
⇒ 2y – 3x = 3 ……(ii)
Multiplying (i) by 3 and subtracting (ii), we get:
3y – 2y = 12 – 3
⇒y = 9
Now, putting y = 9 in (i), we get:
9 – x = 4 ⇒ x = 9 – 4 = 5
Hence, the required fraction is `5/9` .
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