Question

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

Answer 1

Answer :

Let's solve this !

➝The Number will be :

$= \frac{n}{d}$

Here N ➝ Numerator and D ➝ Denominator

➝Let the Numerator be X

Given :

➝Denominator is greater than the Numerator by 8

• Denominator = X + 8

➝ So, Our Number becomes :

• ➝ X / X + 8

Also, Given that if the Numerator is increased by 17 and denominator is decreased by 1 , the Number will be 3/2.

➝ 3/2 = x + 17 / ( X + 8 ) - 1

➝ 3/2 = x + 17 / X +7

Now let's Intercross them !

➝ 3 ( x + 7 ) = 2 ( x + 17 )

➝ 3x + 21 = 2x + 34

➝ 3x = 2x + 34 - 21

➝ 3x = 2x + 13

➝ 3x - 2x = 13

➝ x = 13

Now , The Number was : x / x + 8

➝ 13 / 13 + 8

➝ 13 / 21

So , The Fraction is 13/21 .

Answer 2

Q. The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number

obtained is 3/2, find the fraction.

Conditions :-

• The denominator of a fraction is greater than the numerator by 8.

• If the numerator is increased by 17 and denominator is decreased by 1,

• the number obtained is 3/2,

A/c ,

The Number will be →

$\frac{n}{d} = \frac{numerator}{denominator}$

let,

The numerator be x

A/c :-

• The denominator of a fraction is greater than the numerator by 8.

→ Denominator = x + 8

That is,

The fraction will be →

$\: \: \: \: \: \: \: \: \: \: \: \frac{x}{x + 8}$

• The numerator is increased by 17 and denominator is decreased by 1,

→

$\: \: \: \: \: \: \: \: \frac{x + 17}{(x - 8) - 1}$

• the number so obtained is 3/2

→

$= \frac{3}{2} = \frac{x + 17}{(x + 8) - 1} \\ \frac{3}{2} = \frac{x + 17}{ x + 7} \\ 3(x + 7) = 2(x + 17) \\ 3x + 21 = 2x + 34 \\ 3x - 2x =34 - 21 \\ x = 13$

Now,

Place the value of x = 13 in the fraction →

$\frac{x}{x + 8} = \frac{13}{13 + 8} \\ = \frac{13}{21}$

$\mathtt\blue{Fraction = \frac{13}{21} }$