Question

The denominator of a fraction is $1$ more than its numerator.If $15$ is subtracted from both the numerator and denominator, the fraction becomes $\frac{9}{10}$.Find the fraction.

Answer 1

Let the numerator of the fraction be $x$ then denominator$=x+1$

Fraction$=\frac{Numerator}{Denominator}=\frac{x}{x+1}$

If $15$ is subtracted from both the numerator and the denominator, the new fraction is

$\frac{x-15}{(x+1)-15}=\frac{9}{10}$

$\Rightarrow \frac{x-15}{x-14}=\frac{9}{10}$

$\Rightarrow 10x-150=9x-126$

$\Rightarrow 10x-9x=150-126$

$\Rightarrow x=24$

$\therefore$ Numerator$=x=24$

Denominator$=x+1=24+1=25$

$\therefore$ the fraction is $\frac{24}{25}$