Question

the denominator of fraction us 5 more than numerator ,if the numerator is decreased by two and denominator is increased by 1, the fraction becomes 2/3,find the fraction​

Answer 1

Step-by-step explanation:

let the numerator be $n$.

$\therefore$ denominator will be $n+5$

$\therefore$ fraction is $\frac{n}{n + 5}$

$\because$ now numerator is decreased by $2$ and denominator is increased by $1$ and fraction becomes $\frac{2}{3}$,

$\therefore \frac{n - 2}{n + 5 - 1} = \frac{2}{3}$

=> $\frac{n - 2}{n + 4} = \frac{2}{3}$

=> $3(n - 6) = 2(n + 4)$

=> $3n - 6 = 2n + 8$

=> $3n - 2n = 8 + 6$

=> $n = 14$

$\because$ original fraction was $\frac{n}{n + 5}$ and $n = 14$

$\therefore \frac{n}{n + 5}$

= $\frac{14}{14 + 5}$

= $\frac{14}{19}$