Question

3. The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 2 12 Find the rational 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