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Question
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `1/2`. Find the fraction
Solution
Let the numerator be “x” and the denominator be “y”
∴ The fraction is `x/y`
By the given first condition
x + y = 12 → (1)
Again by the second condition
`x/(y + 3) = 1/2`
2x = y + 3
2x – y = 3 → (2)
(1) + (2) ⇒ 3x = 15
x = `15/3` = 5
Substitute the value of x = 5 in (1)
5 + y = 12
y = 12 – 5
= 7
∴ The fraction is `5/7`
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