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 by 4 find the fraction​

Answer 1

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

First Condition :-

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

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

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)

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

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

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

Put the value of x in First Condition :-

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

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

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

Then :-

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

Answer 2

×+8 3

_________=________

x+11+8 4

=4x+32= 3x+57

=× =57-32=25

fraction 33

_____

44