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 1

Given :

• The sum of the numerator and the denominator of a given fraction is 12.

• 3 is added to its denominator,then the fraction becomes 1/2.

To find :

• The required fraction =?

Step-by-step explanation :

Let, the numerator be, x.

Then, the denominator be, y.

So,

The required fraction be x/y.

It is Given that,

The sum of the numerator and the denominator of a given fraction is 12. So,

x + y = 12 ..... (i)

3 is added to its denominator,then the fraction becomes 1/2.

As per the question :

➟ x/(y + 3) = 1/2

➟ 2 × x = 1(y + 3)

➟ 2x = y + 13

➟ 2x - y = 13 ......(ii)

On adding equation (i) and (ii), we get,

➟ x + y + 2x - y = 3 + 12

➟ 3x = 15

➟ x = 15/3

➟ x = 5.

Therefore, We got the value of, x = 5.

Now,

On putting x = 5 in equation (i) we get,

➟ x + y = 12

➟ 5 + y = 13 [x = 5]

➟ y = 12 - 5

➟ y = 7

Therefore, We got the value of, y = 7.

Hence,

The numerator, x = 5.

And, the denominator, y = 7.

So, The required fraction is 5/7.

Answer 2

$\bf\large{\underline{Question:-}}$

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.

$\bf\large{\underline{Given:-}}$

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

$\bf\large{\underline{To\:find:-}}$

• Given fraction=?

$\bf\large{\underline{Solution:-}}$

Let the Fraction be =$\frac{x}{y}$

we know,

• x+y=12

$\tt→\frac{x}{y+3}=\frac{1}{2}\\\tt→ from\:the\:2nd\: condition \: x=\frac{1}{2}(y+3)$

Now,

into the 1st

$\tt→ \frac{1}{2}(y+3)+y=12\\\tt→ y+3+2y=24\\\tt→ 3y=21\\\tt→ y=\frac{21}{3}\\\tt→ y=7$

From above,

• Given that x+y=12

So,

• putting y=7 in x+y=12

$\tt→ x+y=12\\\tt→ x+7=12\\\tt→ x=12-7\\\tt→ x=5$

Hence,

we consider above that fraction is x/y

therefore,

$\bf{\underline{\fbox{\frac{x}{y}=\frac{5}{7}}}}$