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 :-

The new fraction is 13/21.

Step-by-step explanation:

To Find :-

• The fraction.

★ Solution

Given that,

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

Let us assume the numerator and denominator as (x) and (x + 8) respectively.

• Numerator/Denominator = x/(x + 8)

Also given,

→ The numerator is increased by 17.

→ The denominator is decreased by 1.

Therefore,

Numerator = (x) + 17

= (x + 17)

Denominator = (x + 8) - 1

= (x + 7)

And the number obtained is 3/2.

• (x + 17)/(x + 7) = 3/2

By simplifying,

⇒ (x + 17)/(x + 7) = 3/2

By cross multiplication,

⇒ 2(x + 17) = 3(x + 7)

⇒ 2x + 38 = 3x + 21

⇒ 2x - 3x = 21 - 38

⇒ - 1x = - 13

Cancelling the negative signs [L.H.S & R.H.S],

⇒ 1x = 13 or x = 13

We got, The value of x as 13.

___________________________

According the question,

• The fraction is :-

We assumed the numerator as (x) and denominator as (x + 8),

Therefore, By putting the value of x

⇒ (x)/(x + 8)

⇒ 13/(13 + 8)

⇒ 13/21

Hence The fraction is 13/21.

Answer 2

$\small \mathsf{ \color{purple}{let \: numerator \: be \: x  }}$

$\small \mathsf{ \color{purple}{∴the \: denominator \: will \: be \: x+8 }}$

$⇒x+ \frac{17}{x} +8-1= \frac{3}{2}$

 

$⇒x+ \frac{17}{x} +7= \frac{3}{2}$

$⇒2(x+17)=3(x+7)$

$⇒2x+34=3x+21$

$⇒34-21=3x-2x$

$⇒13=x$

∴x/x+8

$\small \mathsf{ \color{purple}{=13/21     (Ans  )}}$