Question

The denominator of a fraction is five more than the numerator. If 2 is added to both its numerator and denominator, the fraction becomes 6/7
. Find the fraction.

Answer 1

Answer:

Let the numerator be x

Therefore the denominator  is x + 5

So the fraction is x / x +5

Now,

x + 2 / x + 7 = 6 / 7

7x + 14 = 6x + 42

x = 42 - 14

x = 28

Therefore , the reqd. frac is 28/33

Answer 2

Answer:

The fraction is $\rm = \dfrac{28}{33}$

Explanation:

Given,

Denominator of a fraction is 5 more than the numerator.

If we assume numerator as x

Then, denominator will be (x + 5).

$\rm \therefore \: The \: fraction \: = \bf \dfrac{x}{(x + 5)}$

Now,

Adding 2 to both the numerator and denominator.

We get the fraction:

$\rm = \dfrac{(x + 2)}{(x + 5) + 2}$

$\rm = \dfrac{(x + 2)}{(x + 7)}$

According to the question,

$\rm \implies \: \dfrac{(x + 2)}{(x + 7)} = \dfrac{6}{7}$

$\rm \implies \: {7(x + 2)}= {6(x + 7)}$

$\rm \implies \: {7x + 14}= {6x +42}$

$\rm \implies \: {7x - 6x}= {42 - 14}$

$\rm \implies \: {x}= {28}$

Hence, the fraction is,

$\rm = \dfrac{x}{(x + 5)}$

$\rm = \dfrac{28}{(28 + 5)}$

$\rm = \dfrac{28}{33}$

$\underline{ \sf \therefore \:Required \: answer : \dfrac{28}{33} }$