Question

The denominator of a rational number is greater than its numerator by five. If the numerator is increased by eleven and the denominator is decreased by 14, then new number becomes 5, find the original number.

Answer 1

Given that,

the denominator of a rational number is greater than it's numerator by 5.

let the numerator of the rational number be x.

therefore it's denominator = x + 5

ATQ,

when the numerator is increased by 11 and the denominator is decreased by 14, then the number becomes 5.

➡ (x + 11)/(x + 5 - 14) = 5

➡ (x + 11)/(x - 9) = 5

➡ x + 11 = 5(x - 9)

➡ x + 11 = 5x - 45

➡ x - 5x = -45 - 11

➡ -4x = -56

➡ x = -56/-4

➡ x = 14

therefore,

• numerator = x = 14

• denominator = x + 5 = 19

hence, the original number is 14/19.

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer}}}}}}$

Given:-

the denominator of a rational number is greater than its numerator by five,

Let the numerator of the rational number be x

As given in the question : the denominator of a rational number is greater than its numerator by five,

•°•denominator = x + 5

As per the second condition :-

if the numerator is increased by 11 and the denominator is decreased by 14, then new number becomes,

Numerator is increased by 11,

Numerator then becomes : x + 11

denominator is decreased by 14,

Denominator then becomes : x + 5 - 14

We need to find the original number,

Let's begin! :)

$\bf\large{x + 11}{x + 5 - 14}$ = 5

$\bf\large{x + 11}{x - 9}$ = 5

$\bf\large{ <strong>x </strong><strong>+</strong><strong> </strong><strong>11 </strong><strong>=</strong><strong> </strong><strong>5 </strong><strong>(</strong><strong> </strong><strong>x </strong><strong>-</strong><strong> </strong><strong>9</strong><strong>) </strong>}$

$\bf\large{<strong> </strong><strong>x </strong><strong>+</strong><strong> </strong><strong>11 </strong><strong>=</strong><strong> </strong><strong>5x </strong><strong>-</strong><strong> </strong><strong>45</strong>}$

$\bf\large{ <strong>x </strong><strong>-</strong><strong> </strong><strong>5x </strong><strong>=</strong><strong> </strong><strong>-</strong><strong> </strong><strong>45 </strong><strong>-</strong><strong> </strong><strong>11</strong>}$

- 4x = -56

x = $\bf\large\frac{-56}{-4}$

$\bf\large{ <strong>x </strong><strong>=</strong><strong> </strong><strong>14</strong>}$

As per our assumptions,

$\bf{\huge{\underline{\boxed{\rm{\blue{Numerator = x = 14}}}}}}$

$\bf{\huge{\underline{\boxed{\rm{\blue{Denominator = x + 5 = 14 + 5 = 19</p><p>}}}}}}$

Original form of the number = $\bf\large\frac{14}{19}$