Question

The denominator of a fraction is 18 more than the numerator. If 1 is added to both the numerator and denominator, the value of the fraction equals the value of fraction obtained by adding 8 to the numerator and 15 to the denominator. Find the fraction.

Answer 1

Let the fraction be `x/y`.
Given, The denominator of a fraction is 18 more than the numerator.
i.e., x = y - 18
or y - x = 18 ---(1)
Also, If is added to both the numerator and denominator, the value of the fraction equals the value of fraction obtained by adding 8 to the numerator and 15 to the denominator.

⇒ `(x + 1)/(y +1) = (x + 8)/(y +15)`

⇒ `(x + 1 - (y + 1))/(y + 1) = (x + 8 - (y + 15))/(y + 15)`

⇒  `(x - y)/(y + 1) = (x - y - 7)/(y + 15)`

⇒ `(-18)/(y + 1) = (-18 - 7)/(y + 15)`

⇒ `(18)/(y + 1) = (25)/(y + 15)`

⇒ 18y + 18 x 15 = 25y + 25
⇒ 7y = 245
⇒ y = 35.
Hence, x = y - 18 = 35 - 18 = 17

The fraction is `(17)/(35)`.