Question

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Answer 1

Let the numerator = x

and the denominator = y

So, the fraction = x/y

According to the question,

Condition I:

x + y = 2y – 3

⇒ x + y – 2y = – 3

⇒ x – y = – 3 …(i)

Condition II:

⇒ 2(x – 1) = y – 1

⇒ 2x – 2 = y – 1

⇒ 2x – y = 1 …(ii)

On subtracting Eq. (i) from Eq. (ii), we get

2x – y – x + y = 1 + 3

⇒ x = 4

On putting the value of x in Eq. (i), we get

4 – y = – 3

⇒ y = 7

So, the numerator is 4 and the denominator is 7

Hence, the fraction is 4/7.