Question

Numerator of a fraction is 1 more than the denominator. If 2 is added both to the Numerator and denominator, the fraction obtained is $\frac{5}{4}$. Find the fraction.

• A. $\frac{4}{5}$
• B. $\frac{3}{2}$
• C. $\frac{4}{9}$
• D. $\frac{2}{7}$

Answer 1

The correct option is B

$\frac{3}{2}$

Let the denominator be x.

$\therefore$ Numerator is one more than the denominator.

So, Numerator = x + 1

The fraction $=\frac{x+1}{x}$

If 2 is added both to the Numerator and the denominator the fraction becomes $\frac{5}{4}$.

Original fraction $=\frac{x+1}{x}$

Adding 2 to Numerator and denominator,

$\frac{x+1+2}{x+2}=\frac{x+3}{x+2}=\frac{5}{4}\to \text{given}\frac{x+3}{x+2}=\frac{5}{4}$

Cross multiply.

4(x + 3) = 5(x + 2)

4x + 12 = 5x + 10

12 - 10 = 5x - 4x

2 = x

The fraction is $\frac{x+1}{x}$

$\to \frac{2+1}{2}=\frac{3}{2}$