Question

the numerator of a fraction is 8 less than the denominator .if the numerator is increased by 17 and the denominator is decreased by 1,the new fraction obtained is 3/2.find the fraction.​

Answer 1

Given :

• The numerator of a fraction is 8 less than the denominator.
• If numerator is increased by 17 and denominator is decreased by 1 , the fraction obtained is 3/2.

To Find :

• Original Fraction.

Solution :

$\longmapsto\tt{Let\:Denominator\:be=x}$

As Given that the numerator of a fraction is 8 less than the denominator.So ,

$\longmapsto\tt{Numerator=x-8}$

Now ,

• If numerator is increased by 17 and denominator is decreased by 1 , the fraction obtained is 3/2.

$\longmapsto\tt{Numerator=x-8+17}$

$\longmapsto\tt{x+9}$

$\longmapsto\tt{Denominator=x-1}$

A.T.Q :

$\longmapsto\tt{\dfrac{x+9}{x-1}=\dfrac{3}{2}}$

$\longmapsto\tt{2(x-9)=3(x-1)}$

$\longmapsto\tt{2x-18=3x-3}$

$\longmapsto\tt{2x-3x=-3-18}$

$\longmapsto\tt{-1x=-21}$

$\longmapsto\tt\bold{x=21}$

Value of x is 21..

Therefore :

$\longmapsto\tt{Numerator=21-8}$

$\longmapsto\tt\bold{13}$

$\longmapsto\tt\bold{Denominator=21}$

So , The Original fraction is 13/21..

Answer 2

Answer:

13/21

Step-by-step explanation:

If "x" is the denominator, then the numerator is (x - 8) and original fraction is

$\frac{x+9}{x-1}$

If the numerator is increased by 17 and denominator is decreased by 1, then new fraction is

$\frac{(x-8)+17}{x-1}$ = $\frac{3}{2}$

$\frac{x+9}{x-1}$ = $\frac{3}{2}$

3x - 3 = 2x + 18

x = 21

Sought-for fraction is

$\frac{13}{21}$