Question

The denominator of a rational number is greater than its numerator by 3.If numerator is increased by 14 and denominator is is decreased by 3,the new no.become 11/4.What is the original number?​

Answer 1

Let the numerator of rational number be x

It is given that denominator is greater than its numerator by 3

Then,

denominator is x + 3

$= > fraction = \frac{x}{x + 3}$

Now

According to the question,

$\frac{x + 14}{x + 3 - 3} = \frac{11}{4}$

$\frac{x +14}{x} = \frac{11}{4}$

$4(x + 14) = 11x$

$4x + 56 = 11x$

$4x - 11x = - 56$

$- 7x = - 56$

$x = \frac{ - 56}{ - 7}$

$x = 8$

Numerator = 8

Denominator =

$x + 3 = 8 + 3 = 11$

Hence,

Required rational number is

$\frac{8}{11}$