Question

If 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

Answer:-

Let the fraction be x/y.

Given:

If the numerator is multiplied by 2 and denominator is increased by 1 , it becomes 1.

→ 2x/y + 1 = 1

On cross multiplication we get,

→ 2x = y + 1

→ y = 2x - 1 -- equation (1)

And,

The fraction becomes 1/2 if numerator is increased by 4 and denominator is multiplied by 2.

→ x + 4/2y = 1/2

→ 2(x + 4) = 2y

→ 2x + 8 = 2y

Substitute the value of y from equation (1)

→ 2x + 8 = 2(2x - 1)

→ 2x + 8 = 4x - 2

→ 2x - 4x = - 2 - 8

→ - 2x = - 10

→ x = - 10/ - 2

→ x = 5

Substitute x value in equation (1)

→ y = 2(5) - 1

→ y = 10 - 1

→ y = 9

Hence, the required fraction (x/y) is 5/9.