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 ${\displaystyle \frac{1}{2}}$. Find the fraction.

Answer 1

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

So, the Fraction is ${\displaystyle \frac{x}{y}}$

According to the question,

${\displaystyle \frac{2x}{y+1}=1}$

⇒ 2x = y + 1

⇒ 2x - y = 1                  ...(1)

and,

${\displaystyle \frac{x+4}{2y}=\frac{1}{2}}$

⇒ 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 ${\displaystyle \frac{5}{9}}$.