Question

The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, the new number becomes $\frac{3}{2}$. The original number is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let the numerator of a rational number = x

Then the denominator of a rational number = x + 3

When numerator is increased by 7, then new numerator = x + 7

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

The new number formed = $\frac{3}{2}$

So, $\frac{(x+7)}{(x+3-1)}$ = $\frac{3}{2}$

⇒ 3x - 2x = 14 - 6

⇒The numerator of rational number = x = 8

⇒The denominator of rational number = 8 + 3 =11

Fraction = $\frac{8}{11}$