Question

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we add 1 to the denominator. What is 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) = 1

⇒ x + 1 = y – 1

⇒ x – y = – 2

⇒ x – y + 2 = 0 …(i)

Condition II:

x/(y + 1) = 12

⇒ 2x = y + 1

⇒ 2x – y = 1

⇒ 2x – y – 1 = 0 …(ii)

By cross - multiplication method, we have

On taking I and III ratio, we get

⇒ x/3 = 1/1

⇒ x = 3

On taking II and III ratio, we get

⇒ y/5 = 1/1

⇒ y = 5

So, the numerator is 3 and the denominator is 5

Hence, the fraction is 3/5.