Question

The denominator of a fraction is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new fraction is 1/5 . The sum of the numerator and the denominator of the original fraction is

Answer 1

Answer :

The sum of the numerator and the denominator of the original fraction is 13.

Given :

• The denominator of a fraction is greater than its numerator by 3.
• If 3 is subtracted from the numerator and 2 is added to the denominator, the new fraction is 1/5.

To find :

• Sum of the numerator and the denominator of the original fraction.

Solution :

Consider,

• Numerator of the fraction = x

★ The denominator of the fraction is greater than its numerator by 3.

Then,

• Denominator of the fraction = (x+3)

★ If 3 is subtracted from the numerator and 2 is added to the denominator, the new fraction is 1/5.

According to the question :-

$\to \sf \: \dfrac{x - 3}{x + 3 + 2} = \dfrac{1}{5}$

$\to \sf \: \dfrac{x - 3}{x + 5} = \dfrac{1}{5}$

$\to \sf \: 5x - 15 = x + 5$

$\to \sf \: 5x - x = 5 + 15$

$\to \sf \: 4x = 20$

$\to \sf \: x = \dfrac{20}{4}$

$\to \sf \:x = 5$

• Numerator = 5

Then,

• Denominator = (5+3) = 8

Therefore,

The sum of the numerator and the denominator of the original fraction,

= 5 + 8

= 13

Answer 2

$\huge{\boxed{\bf{\red{Given }}}}\::$

• The denominator of a fraction is greater than its numerator by 3.
• If 3 is subtracted from the numerator and 2 is added to the denominator, the new fraction is 1/5.

$\huge{\boxed{\bf{\blue{To \ find }}}}\::$

• Sum of the numerator and the denominator of the original fraction.

$\huge{\boxed{\bf{\purple{Solution }}}}\::$

Let,

• Numerator of the fraction be $\bf{ x }$

★ The denominator of the fraction is greater than its numerator by 3.

Then,

Denominator of the fraction = (x+3)

★ If 3 is subtracted from the numerator and 2 is added to the denominator, the new fraction is 1/5.

A.T.Q :-

$\mapsto \: \sf\orange{ \dfrac{x - 3}{x + 3 + 2} = \dfrac{1}{5}}$

$\mapsto\: \sf \blue{ \dfrac{x - 3}{x + 5} = \dfrac{1}{5}}$

$\mapsto \:\sf \orange{5x - 15 = x + 5}$

$\mapsto \:\sf\blue{ 5x - x = 5 + 15}$

$\mapsto\: \sf \orange{ 4x = 20}$

$\mapsto\: \sf\blue{x = \dfrac{20}{4}}$

$\mapsto \sf \orange{x = 5}$

★ Denominator of the fraction = (x+3)

☞ Denominator = (5+3) = 8

Hence, The sum of the numerator & Denominator of the original fraction,

↠ 5 + 8

↠ $\bf\pink{13}$