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. 8/11
• B. 5/8
• C. 7/10
• D. 2/5

Answer 1

The correct option is A

8/11

Let the numerator of the rational number be x
Then the denominator is (x + 3)
When the numerator is increased by 7, it becomes (x + 7)
When the denominator is decreased by 1, it becomes (x + 3 - 1)

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

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

⇒ 3x - 2x = 14 - 6

⇒ x = 8

⇒The numerator of the rational number = 8

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

Hence, the original fraction is $\frac{8}{11}$.