Question

5. The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is ³/2. Find the rational number.​

Answer 1

Correct Question :-

The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

Answer:-

The required rational number is 11/21.

Step-by-step explanation

To Find :-

• The rational number.

★ Solution

Given that,

The denominator of a rational number is greater than it's numerator by 10.

Assumption

Let us assume the numerator & denominator as (x) and (x + 10) respectively.

Also given,

The numerator is increased by 19 and the denominator is decreased by 1. The new rational number is 3/2.

According the question,

Numerator = (x) + 19 = (x + 19)

Denominator = (x + 10) - 1 = (x + 9).

∴ (x + 19)/(x + 9) = 3/2

By simplifying,

⇒ (x + 19)/(x + 9) = 3/2

⇒ 3(x + 9) = 2(x + 19)

⇒ 3x + 27 = 2x + 38

⇒ 3x - 2x + 27 = 38

⇒ 3x - 2x = 38 - 27

⇒ x = 38 - 27

⇒ x = 11

The value of x is 11.

__________________________

Finding, The numerator and denominator-

Numerator :-

We assumed the numerator as (x).

⇒ x

⇒ 11

Denominator :-

We assumed the denominator as (x + 10).

⇒ (x + 10)

⇒ (11 + 10)

⇒ 21

Therefore, The fraction is - 11/21.