Question

please helpThe denominator of a fraction exceeds the numerator by 5. If 3 be added to
both, the fraction becomes 3/4. Find the fraction.

Answer 1

• The fraction = $\sf \dfrac{12}{17}$

Given :

• The denominator of a fraction exceeds the numerator by 5.
• If 3 be added to both, the fraction = $\sf \dfrac{3}{4}$

To Find :

• The fraction.

Solution :

Let,

The numerator be x.

The denominator be x + 5 because according to the question, the denominator of a fraction exceeds the numerator by 5.

Now the fraction is,

$\implies \dfrac{x}{x + 5}$

According to the condition,

If 3 be added to both sides (numerator and denominator) then the fraction will be $\sf \dfrac{3}{4}$

$\implies \dfrac{x + 3}{x + 5 + 3} = \dfrac{3}{4}$

First, we need to find the value of x.

$\implies \dfrac{x + 3}{x + 8} = \frac{3}{4}$

$\implies4(x + 3) = 3(x + 8)$

$\implies4x + 12 = 3x + 24$

$\implies4x - 3x = 24 - 12$

$\implies 1x = 12$

$\implies x = 12$

Now, we have to find the fraction.

So, substitute the value of x in equation (1),

$\implies \dfrac{x}{x + 5}$

$\implies \dfrac{12}{12 + 5}$

$\implies \dfrac{12}{17}$

Hence,

The fraction is $\sf \dfrac{12}{17}$

Verification :

If 3 be added to both sides of a fraction, the fraction = $\sf \dfrac{3}{4}$

Now we have,

• Fraction = $\sf \dfrac{12}{17}$

$\implies \dfrac{12 + 3}{17 + 3} = \dfrac{3}{4}$

$\implies\cancel \dfrac{15}{20} = \dfrac{3}{4}$

$\implies \dfrac{3}{4} = \dfrac{3}{4}$

Hence Proved !!