Question

The denomination of a rational number is greater than its numerator by 8 if the number is increased by 17 and denomination is decreased by 1 , the number obtained is 3/2. Find the number​

Answer 1

Answer:

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be \(\frac{x}{x+8}\)

According to the given condition,

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

\(\frac{x+17}{x+7} = \frac{3}{2}\)

3(x + 7) = 2(x + 17)

3x + 21 = 2x + 34

3x – 2x + 21 – 34 = 0

x – 13 = 0

x = 13

The rational number will be

= \(\frac{x}{x+8}\)

= \(\frac{13}{13+8}\)

Rational number = 13/21

Answer 2

Answer

Let the numerator be x.

Let the denominator be x + 8.

So, the fraction becomes

$\sf \dashrightarrow \dfrac{x}{x + 8}$

We are given that,

The numerator is increased by 17 and denominator is decreased by 1. The fraction obtained while calculating the numerator and denominator is,

$\sf \dashrightarrow \dfrac{3}{2}$

According to the question,

Numerator of the fraction :

$\sf \dashrightarrow \dfrac{x + 17}{(x + 8) - 1} = \dfrac{3}{2}$

$\sf \dashrightarrow 2(x + 17) = 3(x + 8 - 1)$

$\sf \dashrightarrow 2(x + 17) = 3(x + 7)$

$\sf \dashrightarrow 2x + 34 = 3x + 21$

$\sf \dashrightarrow 2x - 3x = 21 - 34$

$\sf \dashrightarrow -1x = -13$

$\sf \dashrightarrow x = \dfrac{-13}{-1}$

$\sf \dashrightarrow x = 13$

Now, let's find the value of denominator.

Denominator of the fraction :

$\sf \dashrightarrow x + 8$

$\sf \dashrightarrow 13 + 8$

$\sf \dashrightarrow 21$

So, the fraction becomes 13/21.

Hence, the original rational number is 13/21.