Question

Numerator of a fraction is 5 more than its

denominator' If 4 is added to numerator

and denominator the fraction obtained is 6/5 find the original fraction​

Answer 1

Answer :-

• The original fraction is $\sf{\dfrac{26}{21}}$.

Step-by-step explanation:

To Find :-

• The original fraction

Solution:

Given that,

Assumption:

Let us consider the numerator and denominator as :-

• Denominator = ( x )

Given,

Numerator of a fraction is 5 more than its denominator, therefore numerator is

• Numerator = ( x + 5 ),

Therefore, The fraction is :-

$\underline{\boxed{\sf{\dfrac{(x + 5)}{x}}}}$

Also given,

• If 4 is added to numerator and denominator the fraction obtained is $\sf{\dfrac{6}{5}}$.

Therefore,

$\underline{\boxed{\sf{\dfrac{(x + 5) + 4}{x + 4} = \dfrac{6}{5}}}}$

By evaluating,

$\implies \: \sf{\dfrac{(x + 5) + 4}{x + 4} = \dfrac{6}{5}}$

$\implies \: \sf{\dfrac{x + 9}{x + 4} = \dfrac{6}{5}}$

$\implies \: \sf{6(x + 4) = 5(x + 9)}$

$\implies \: \sf{6x + 24 = 5(x + 9)}$

$\implies \: \sf{6x + 24 = 5x + 45}$

$\implies \: \sf{6x - 5x = 45 - 24}$

$\implies \: \sf{x = 21}$

Therefore, The original fraction is :-

$\longrightarrow \: \sf{\dfrac{(x + 5)}{x}}$

$\longrightarrow \: \sf{\dfrac{(21 + 5)}{21}}$

$\longrightarrow \: \boxed{ \sf{\dfrac{26}{21}}} \: \bigstar$

Hence, the original fraction is $\sf{\dfrac{26}{21}}$.