Question

The sum of the numerator and the denominator of a given fraction is 12. If 3 is added to its denominator,
then the fraction becomes 12. Find the given fraction.​

Answer 1

Question:

The sum of the numerator and the denominator of a given fraction is 12. If 3 is added to its denominator, then the fraction becomes 1/2. Find the given fraction.

Answer:

The required fraction is 5/7.

Solution:

Let the numerator and the denominator of the fraction be N and D respectively.

Thus,

The fraction will be N/D

It is given that,

The sum of the numerator and the denominator of the fraction is 12.

Thus,

=> N + D = 12

=> N = 12 - D ---------(1)

Now,

According to the question,

If 3 is added to the denominator of the fraction,

then the fraction becomes 1/2.

Thus,

=> N/(D+3) = 1/2

=> (12-D)/(D+3) = 1/2

=> 2•(12-D) = 1•(D+3)

=> 24 - 2D = D + 3

=> 2D + D = 24 - 3

=> 3D = 21

=> D = 21/3

=> D = 7

Now,

Putting D = 7 in eq-(1) , we get;

=> N = 12 - D

=> N = 12 - 7

=> N = 5

Hence,

The required fraction is N/D ,ie; 5/7.

Answer 2

Correct Question :----

• sum of Numerator and denominator = 12 .
• If 3 is added to denominator the fraction becomes 1/2 .

To Find :-----

• The original Fraction ?

Solution :-----

$\textbf{Let the Original Fraction be} \\ { \red{\frac{N} {D}} ..} \: \\ \\ given \\ \\ N + D = 12 \\ \\ \red\leadsto \: D \: = (12 - N)$

_______________________________

Now, it Has been said that, 3 is added to Denominator D ,

and our Fraction becomes 1/2 ,

so,

A/q,

$\frac{N}{ D + 3} = \frac{1}{2} \\ \\ Putting \: D = (12 - N) \: we \: get \\ \\ \red\leadsto \: \frac{N}{ (12 - N) + 3} = \frac{1}{2} \\ \\ \red\leadsto \: \frac{N}{ 15 - N} = \frac{1}{2} \\ \\ cross - multiplying \\ \\ \red\leadsto \: 2N \: = (15 - N) \\ \\ \red\leadsto \: \: 3N = 15 \\ \\\red\leadsto \: N \: = \frac{15}{3} \\ \\ \large\boxed{\bold{N = 5}}$

____________________

Now,

since N + D = 12

= 12 Hence,

= 12 Hence,Putting value of N , we get,

$D = 12 - 5 \\ \\ \large\boxed{\bold{D = 7}}$

___________________________

$\green{\textbf{Hence, our Original Fraction is }} \\ \pink{\large\boxed{\boxed{\bold{ \frac{5}{7} }}}}$

$\large\underline\textbf{Hope it Helps You.}$