Question

In a fraction, if numerator is increased by 2 and denominator is decreased by 3, then the fraction becomes 1. Instead, if numerator is decreased by 2 and denominator is increased by 3, then the fraction becomes $\frac{3}{8}$. Find the fraction.

Answer 1

Let the fraction be $\frac{a}{b}$.

Therefore, $\frac{a+2}{b-3}=1$

$a+2=b-3$

$a-b=-5$ .......(1)

Also, $\frac{a-2}{b+3}=\frac{3}{8}$

$8a-16=3b+9$

$8a-3b=25$

Solving these equations, we get,

$a=8$ and $b=13$

Thus, the fraction is $\frac{8}{13}$.

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