Question

The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes 3/4 .Find fraction

Answer 1

answer: fraction is 25/36

Step-by-step explanation: Given :the denominator of a fraction is greater than its numerator by 11. if 8 is added to both its numerator & denominator, it becomes 3/4.

To find : the fraction.

 

Let x be the numerator and y be the denominator.

Hence the fraction is x/y.

 

Now acc to question,  

the denominator of a fraction is greater than its numerator by 11.  

=> y = x + 11........................................(1)

 

if 8 is added to both its numerator & denominator, it becomes 3/4.

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

=> 4x - 3y = -8 .....................................(2)

Now substituting y from eq (1) to eq (2) , we get  

we get x = 25  

 

y= x+ 11

=> y = 25+11 = 36

Therefore the fraction is = x/y = 25 /36  

Answer 2

Given,

• The denominator of fraction is greater then its numerator by 11.
• If 8 is added to both its numerator and denominator then it becomes 3/4.

To Find,

• The Fraction

Solution,

⇒Suppose the numerator be x

And , Suppose the denominator be y

According to the First Condition :-

• The denominator of fraction is greater then its numerator by 11.

$\implies \boxed{\sf{y = x + 11}}$

According to the Second Condition :-

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

$\implies \sf{\dfrac{x + 8}{y + 8} = \dfrac{3}{4}}$

$\implies \sf{4(x + 8) = 3(y + 8) }$

$\implies \sf{4x + 32 = 3y + 24}$

$\implies \sf{4x - 3y = 24 - 32}$

$\implies \sf{4x - 3y = -8}$

$\implies \sf{4x -3( x + 11) = -8}$

(Put the value of y From the First Condition)

$\implies \sf{4x -3x - 33 = -8}$

$\implies \sf{x = -8 + 33}$

$\implies \boxed{\sf{ x = 25}}$

Now Put the value of x in First Condition :-

$\implies \sf{ y = x + 11}$

$\implies \sf{ y = 25 + 11}$

$\implies \boxed{\sf{ y = 36}}$

Therefore,

$\boxed{\sf{\red{The \ Fraction = \dfrac{25}{36}}}}$

$\rule{200}2$