Question

The sum of numerator and denominator of a fraction is 30. If 2 is

added to numerator and 2 is subtracted from denominator, then it

becomes 2/3. Find the fraction.​

Answer 1

Given :

The sum of numerator and denominator of a fraction is 30. If 2 is  added to numerator and 2 is subtracted from denominator, then it  becomes 2/3

To Find :

Fraction

Solution :

Let ,

• numerator be x
• denominator be y

So , fraction becomes  $\sf \dfrac{x}{y}$  .

The sum of numerator and denominator of a fraction is 30

⇒ x + y = 30

⇒ x = 30 - y ... (1)

If 2 is  added to numerator and 2 is subtracted from denominator , then it becomes 2/3

$\to \sf \dfrac{x+2}{y-2}=\dfrac{2}{3}$

sub. (1) here ,

$\to \sf \dfrac{(30-y)+2}{y-2}=\dfrac{2}{3}\\\\\to \sf \dfrac{32-y}{y-2}=\dfrac{2}{3}\\\\\to \sf 3(32-y)=2(y-2)\\\\\to \sf 96-3y=2y-4\\\\\to \sf 5y=100\\\\\leadsto \sf \pink{y=20}\ \; \bigstar$

Sub. y value in (1) ,

⇒ x = 30 - (20)

⇒ x = 10  $\green{\bigstar}$

So , Fraction is ,  $\sf \purple{\dfrac{x}{y} =\dfrac{10}{20}}\ \; \bigstar$

Answer 2

☆Answer:☆

______________________________

Let the numerator be n and denominator be d.

According to the question,its given that :

n + d = 30

$\frac{n + 2}{d - 2} = \frac{2}{3}$

=>3(n+2) = 2(d-2)

=>3n +6 = 2d -4;

=>3n - 2d = -10 ________Equation 1

And,

n + d = 30

n = 30 - d ___________Equation 2

Now,upon using Equation 2 in Equation 1 we get ;

3(30 - d) - 2d = -10

90 - 3d - 2d = -10

90 - 5d = -10

- 5d = -10 - 90

- 5d = -100

d = 20

On putting the value of d = 20 in Equation 2 we have ;

n = 30 - d

n = 30 - 20

n = 10

$Therefore, \: the \: fraction \: is \: \frac{10}{20} or \: \frac{1}{2} .$

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