Question

the denominator of a fraction is greater than its numerator by 4. if 5 is added in the numerator and denominator then the fraction becomes equivalent to 2/3, then find the denominator of the original fraction.
options are (1) 9 (2) 7 (3)8 (4)11
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Answer 1

Answer:

option 2

Step-by-step explanation:

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Answer 2

The denominator of the original fraction = 7

Given :

• The denominator of a fraction is greater than its numerator by 4.

• If 5 is added in the numerator and denominator then the fraction becomes equivalent to 2/3

To find :

The denominator of the original fraction is

(1) 9

(2) 7

(3) 8

(4) 11

Solution :

Step 1 of 2 :

Form the equation to find the denominator of the original fraction

Let numerator of the fraction = x

Since denominator of a fraction is greater than its numerator by 4.

So denominator of the fraction = x + 4

$\displaystyle \sf The \: fraction = \frac{x}{x + 4}$

Now it is given that when 5 is added in the numerator and denominator then the fraction becomes equivalent to 2/3

So by the given condition

$\displaystyle \sf \frac{x + 5}{x + 4 + 5} = \frac{2}{3}$

Step 2 of 2 :

Calculate the denominator of the original fraction

$\displaystyle \sf \frac{x + 5}{x + 4 + 5} = \frac{2}{3}$

$\displaystyle \sf{ \implies \frac{x + 5}{x + 9} = \frac{2}{3} }$

$\displaystyle \sf{ \implies 3(x + 5) = 2(x + 9)}$

$\displaystyle \sf{ \implies 3x + 15= 2x + 18}$

$\displaystyle \sf{ \implies 3x - 2x= 18 - 15}$

$\displaystyle \sf{ \implies x= 3}$

Numerator of the original fraction = x = 3

Denominator of the original fraction

= x + 4

= 3 + 4

= 7

Hence the correct option is (2) 7

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