Question

lf the numerator of a fraction is multiplied by 2 and its denominator is increased by 1, it becomes 1. However, if the numerator is increased by 4 and denominator is multiplied by 2, the fraction becomes `1/2`. Find the fraction.

Answer 1

Let the numerator of the fraction be x and the denominator be y.

So, the Fraction is `x/y`

According to the question,

`[2x]/[ y + 1 ] = 1`

⇒ 2x = y + 1

⇒ 2x - y = 1                  ...(1)

and,

`[ x + 4 ]/[2y] = 1/2`

⇒ 2x + 8 = 2y

⇒ 2x - 2y = - 8                ...(2)

Solving equations (1) and (2), We get

y = 9

Putting the value of y in (1), we get

2x - 9 = 1

⇒ 2x = 1 + 9

⇒ x = 5

So, the fraction is `5/9`.