Question

The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator

the fraction increases by unity. The fraction is.​

Answer 1

Answer:

Let numerator be x.

Let denominator be x+2.

fraction = (x+2)

$\sf \: \frac{(x + 5)}{(x + 2)} = \frac{x}{(x + 2)} +1$

$\sf \implies \frac{(x + 5)}{(x + 2)} - \frac{x}{(x + 2)} =1$

$\sf \implies \frac{(x + 5 - x)}{(x + 2)} = 1$

$\sf \implies \: \frac{5}{(x + 2)} = 1$

• By Cross multiplication, we get

$\sf \implies 5 = x+2$

$\sf \implies \: 5-2 = x$

$\sf \implies \: x=3$

The fraction is $\sf \frac{3}{5}$.