Question

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 3÷2.Find the rational number.​

Answer 1

Answer :-

Let the numerator be x.

According to the question,

$\implies \sf \dfrac{x}{x+8}$ is the number.

If the numerator is increased by 17 and the denominator is decreased by 1, $\longrightarrow \sf \dfrac{x+17}{(x+8)-3}$ is the rational number formed.

The number obtained is $\sf \dfrac{3}{2}$.

By forming the equation,

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

By cross multiplying, we get,

→ 2(x + 17) = 3{(x + 8) - 3}

→ 2x + 34 = 3(x + 8 - 3)

→ 2x + 34 = 3(x + 5)

→ 2x + 34 = 3x + 15

Taking 2x to the other side,

→ 34 = 3x + 15 - 2x

Taking 15 to the other side

→ 34 - 15 = 3x - 2x

→ 19 = x

Therefore the rational number is $\sf \dfrac{19}{27}$