Question

The denominator of a rational number is greater than its numerator by 3.If the numerator is increased by 8 and the denominator is decreased by 1, then new number becomes $\frac{5}{3}$.The original number is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the numerator of rational number = x

Denominator of a rational number = x + 3

When numerator is increased by 8, then new numerator = x + 8

When denominator is decreased by 1, then new denominator = x + 3 - 1 = x + 2

New number = $\frac{5}{3}$

$\Rightarrow$ $\frac{x+8}{x+2}$ = $\frac{5}{3}$
$\Rightarrow$ 3x + 24 = 5x + 10
$\Rightarrow$ 2x = 14
$\Rightarrow$ x = 7

So, the original number will be $\frac{7}{10}$