Question

THE denominator of a fraction is greater than itss numerator by 11. if 8 is added to both its numerator and denominator, it becomes 3/4. find the fraction

Answer 1

Let us assume, x and y are the numerator and denominator of a fraction x/y

Given:

y = x + 11

y – x = 11---------------1

Also given:

x + 8 / y + 8 = 3/4

4 (x + 8) = 3 (y + 8)

4x + 32 = 3y + 24

3y – 4x = 8 ----------2

Multiply equation 1 by 3

3y – 3x = 33 ------------3

Subtract eqn 2 from eqn 3

x = 25

Therefore, y = x + 11 = 25 + 11 = 36

Therefore, fraction is = 25/36

Answer 2

Answer:

Step-by-step explanation:

Given :-

The denominator of a fraction is greater than itss numerator by 11.

If 8 is added to both its numerator and denominator, it becomes 3/4.

To Find :-

The fraction

Solution :-

Let the required fraction be x/y .  

According to the Question

1st Equation

⇒ y = x + 11  

⇒ y – x = 11 ……(i)  

2nd Equation

⇒ x+8/y+8 = 3/4  

⇒ 4(x + 8) = 3(y + 8)  

⇒ 4x+ 32 = 3y + 24  

⇒ 4x – 3y = -8 ……(ii)  

On multiplying Equation(i) by 4

4y – 4x = 44  

On adding Eq (ii) and (iii)

⇒ y = (-8 + 44)

⇒ y = 36  

On substituting y = 36 in (i), we get:  

⇒ y – x = 11

⇒ 36 – x = 11  

⇒ x = (36 – 11)

⇒ x = 25  

Hence, the required fraction is 25/36 .