Question

The denominator of a fraction exceeds the numerator by 2. If 5 be added
to the numerator the fraction increases by unity. The fraction is
​

Answer 1

Answer:

Let the fraction be p/q

It is given q = p +2 and

(p+5)/q = p/q +1 = (p + q)/q

p+5 = p+q

q = 5

p = q - 2 = 3

So fraction = 3/5 Ans

Answer 2

Given:

• The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.

To Find

• What is the Fraction?

Solution:

Let the numerator be x

Denominator be (x + 2)

Then,

Fraction be ${\tt{ \left( \dfrac{x}{x+2} \right) }}$

Again,

Adding 5 in the numerator of the fraction it is increased by unity

Fraction be ${\tt{ \left( \dfrac{x+5}{x+2} \right) }}$

According to Question,

$\colon\implies{\tt{ \dfrac{x+5}{x+2} = \dfrac{x}{x+2} + 1 }} \\ \\ \\ \colon\implies{\tt{ \dfrac{x+5}{ \cancel{x+2} } = \dfrac{x+(x+2)}{ \cancel{x+2} } }} \\ \\ \\ \colon\implies{\tt{ (x+5) = x+(x+2) }} \\ \\ \\ \colon\implies{\tt{ x+ 5 = 2x + 2 }} \\ \\ \\ \colon\implies{\tt{ 5 - 2 = 2x - x }} \\ \\ \\ \colon\implies{\boxed{\mathfrak\purple{ x = 3 }}}$

Therefore,

The Fraction will be

${\tt{ \left( \dfrac{x}{x+2} \right) = \dfrac{3}{3+2} }} \\ \\ \colon{\boxed{\tt\red{ \dfrac{3}{5} }}}$

Hence,

• The Fraction is 3/5 .