Question

The denominator of a rational number is greater than its numerator by 6 .if the numerator is increased by 15 and denominator by 1 then the obtained number is 3 by 2 find the rational number

Answer 1

Answer:

Answer is 26 x .

Full answer is photo below.

Step-by-step explanation:

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Answer 2

⇒ Given:

The denominator of a rational number is greater than its numerator by 6.

When the numerator is increased by 15 and denominator by 1 then the obtained rational number is 3/2.

⇒ To Find:

The rational number.

⇒ Solution:

Let the numerator of the number be x. This means that the denominator of the rational number is x + 6.

$\sf{\implies\:Rational\:number=\dfrac{x}{x+6}}$

It is given that that when the numerator is increased by 15 and the denominator by 1, the rational number is 3/2.

$\sf{\implies\:\dfrac{x+15}{x+6+1}=\dfrac{3}{2}}$

$\sf{\implies\:\dfrac{x+15}{x+7}=\dfrac{3}{2}}$

Doing cross multiplication:

$\sf{\implies\:2(x+15)=3(x+7)}$

$\sf{\implies2x+30=3x+21}$

$\sf{\implies\:30-21=3x-2x}$

$\sf{\implies\:x=9}$

This means that,

→ The numerator of the rational number is x which is 9.

→ The denominator of the rational number is x + 6 which is 15.

The required rational number is 9/15.

Rational Number:

A number in the form p/q where p and q are integers and q ≠ 0 is termed as a rational number. Rational numbers were discovered by the mathematician Pythagoras.