Question

If 1 is added to the denominator of a fraction, the fraction becomes `(1)/(2)`. If 1 is added to the numerator of the fraction, the fraction becomes 1. Find the fraction.

Answer 1

Let the numerator and denominator of a fraction be x and y respectively.
∴ Fraction = `x/y`
According to given information, we have
`(x)/(y + 1) = (1)/(2)`
⇒ 2x = y + 1
⇒ 2x - y = 1  ....(i)
Also,
`(x + 1)/y = 1`
⇒ x + 1 = y
⇒ x - y = -1  ....(ii)
Subtracting eqn. (ii) from (i), we get
x = 2
⇒ 2 - y = -1
⇒ y = 3
∴ Required fraction = `(2)/(3)`.