Question

The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator, and denominator both, the fraction becomes \[\frac{2}{3}\]. Find the original fraction.

Answer 1

Let denominator of the original fraction = x

Then numerator = x – 5

and fraction = `("x" - 5)/"x"`

According to the condition,

`("x" - 5 + 3)/("x" + 3) = 4/5`

`=> ("x" - 2)/("x" + 3) = 4/5`

⇒ 5(x - 2) = 4x + 12

⇒ 5x - 10 = 4x + 12

⇒ x = 22

∴ Original fraction = `("x" - 5)/"x"`

`= (22 - 5)/22 = 17/22`