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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 and denominator of a fraction be x and y respectively.
∴ Fraction = `x/y`
According to given information, we have
x + y = 12 ....(i)
And,
`(x)/(y + 3) = (1)/(2)`
⇒ 2x = y + 3
⇒ 2x - y = 3 ....(ii)
Adding eqns. (i) and (ii), we get
3x = 15
⇒ x = 5
⇒5 + y = 12
⇒ y = 7
∴ Required fraction = `(5)/(7)`.
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