Question

The sum of the numerator and
denominator of a fraction is 12if
the denominator is increase by 3
the fraction becomes 1/2 find the
fraction​

Answer 1

Answer:

Given : The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2.

To find : What is the fraction?

Solution : Let the fraction is  

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

.........[1]

→ If the denominator is increased by 3, the fraction becomes 1/2.

 .........[2]

Put the value of x from [1] in [2]

Put back the value of y in [1]

Therefore, The required fraction is

Step-by-step explanation:

Answer 2

Given :

• Sum of Numerator and Denominator = 12.

• Fraction when denominator is increased by 3 = ½.

To Find :

The orginal Fraction.

Solution :

Let the Numerator and Denominator be x and y respectively.

So , according to the fraction formed is $\bf{\dfrac{x}{y}}$

We also know the sum of the Numerator and Denominator i.e, 12.

Hence, the Equation formed is :-

$\underline{\therefore \bf{x + y = 12}}\:\:\:\:(Equation.i)$

Now according to the Question , it said that the fraction becomes ½ , when is 3 is added to both the Numerator and Denominator.

So , the equation formed is :-

$:\implies \bf{\dfrac{x}{y + 3} = \dfrac{1}{2}}$

By solving it, we get :-

$:\implies \bf{\dfrac{x}{y + 3} = \dfrac{1}{2}}$

By multiplying 2 on both the sides , we get :

$:\implies \bf{\dfrac{x}{y + 3} = \dfrac{1}{2}}$

$:\implies \bf{\dfrac{x}{y + 3} \times 2 = \dfrac{1}{2} \times 2}$

$:\implies \bf{\dfrac{x}{y + 3} \times 2 = \dfrac{1}{\not{2}} \times \not{2}}$

$:\implies \bf{\dfrac{2x}{y + 3} = 1}$

Now, by multiplying (y + 3) on both the sides, we get :

$:\implies \bf{\dfrac{2x}{y + 3} \times (y + 3) = 1 \times (y + 3)}$

$:\implies \bf{2x = y + 3}$

By subtracting y from both the sides , we get :

$:\implies \bf{2x - y = y + 3 - y}$

$:\implies \bf{2x - y = \not{y} + 3 - \not{y}}$

$:\implies \bf{\dfrac{x}{y}}$

$:\implies \bf{2x - y = 3}$

$\underline{\therefore \bf{2x - y = 3}}\:\:\:(Equation.ii)$

Now , by adding Equation (i) from Equation (ii) , we get :

$:\implies \bf{(x + y) + (2x - y) = 12 + 3}$

$:\implies \bf{x + y + 2x - y = 12 + 3}$

$:\implies \bf{x + y + 2x - y = 15}$

$:\implies \bf{x + \not{y} + 2x - \not{y} = 15}$

$:\implies \bf{x + 2x = 15}$

$:\implies \bf{3x = 15}$

$:\implies \bf{x = \dfrac{15}{3}}$

$:\implies \bf{x = 5}$

Hence, the value of x is 5.

Now , Substituting the value of x in Equation (i) , we get :

$:\implies \bf{x + y = 12}$

$:\implies \bf{5 + y = 12}$

$:\implies \bf{y = 12 - 5}$

$:\implies \bf{y = 7}$

Hence, the value of y is 7.

Since, we have taken x as the Numerator and y as the denominator.

The orginal Fraction is :-

$:\implies \bf{\dfrac{x}{y}}$

Putting the value of x and y in the above equation, we get:

$:\implies \bf{\dfrac{5}{7}}$

$\boxed{\therefore \bf{Original\:Fraction = \dfrac{5}{7}}}$

Hence the original Fraction is 5/7.