Question

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Answer 1

Let the numerator = x

and the denominator = y

So, the fraction = x/y

According to the question,

Condition I:

(x - 1)/y = 1/3

⇒ 3(x – 1) = y

⇒ 3x – 3 = y

⇒ 3x – y – 3 = 0 …(i)

Condition II:

x/(y + 8) = 1/4

⇒ 4x = y + 8

⇒ 4x – y = 8

⇒ 4x – y – 8 = 0 …(ii)

By cross - multiplication method, we have

On taking I and III ratio, we get

x/5 = 1/1

⇒ x = 5

On taking II and III ratio, we get

y/12 = 1/1

⇒ y = 12

So, the numerator is 5 and the denominator is 12

Hence, the fraction is 3/5.