Question

The denominator of a rational number is greater than its numerator by 3. If
numerator and denominator are increased by 1 and 4, respectively, the number
obtained is Find the rational number.
(4
1
2
1​

Answer 1

Answer:

Correct Question :-

The denominator of a rational number is greater than its numerator by 3. If numerator and denominator are increased by 1 and 4 respectively. The number obtained is ½. Find the rational number.

Given :-

The denominator of a rational number is greater than its numerator by 3. If numerator and denominator are increased by 1 and 4 respectively. The number obtained is ½.

To Find :-

What is the rational number.

Solution :-

Let, the numerator be x

And, the denominator will be x + 3

Then, the rational number is $\sf \dfrac{x}{x + 3}$

According to the question,

↦ $\sf \dfrac{x + 1}{x + 3 + 4} =\: \dfrac{1}{2}$

↦ $\sf \dfrac{x + 1}{x + 7} =\: \dfrac{1}{2}$

By doing cross multiplication we get,

↦ $\sf 2(x + 1) =\: 1(x + 7)$

↦ $\sf 2x + 2 =\: x + 7$

↦ $\sf 2x - x =\: 7 - 2$

➠ $\sf\bold{\green{x =\: 5}}$

Hence, the required rational number is :-

➲ $\sf \dfrac{x}{x + 3}$

⇒ $\sf \dfrac{5}{5 + 3}$

➦ $\sf\bold{\purple{\dfrac{5}{8}}}$

$\therefore$ The rational number is $\sf\boxed{\bold{\red{\dfrac{5}{8}}}}$.