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 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 numerator of the rational number be $x.$
Then denominator of the rational number can be written as $(x+3)$

Thus the rational number is $\frac{x}{x+3}$
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, $\frac{(x+7)}{(x+2)}=\frac{3}{2}$

By cross multiplication,

⇒$2(x+7)=3(x+2)$

⇒ $2x+14=3x+6$
⇒ $(3x-2x)=(14-6)$ [Grouping like terms]

⇒$x=8$

⇒The numerator of the rational number $=x=8$

⇒ The denominator of the rational number = $(x+3)=8+3=11$

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