Question

The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1 3 of it. Find the original fraction.

Answer 1

Answer:

The original fraction is $\frac{3}{8}$

Step-by-step explanation:

Let the denominator be x

We are given that The numerator of a fraction (which is in its simplest form) is 5 less than the denominator.

Numerator = x-5

So, Fraction =$\frac{x-5}{x}$

If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1\3 of it.

A.T.Q

$\frac{2(x-5)}{x+16}=\frac{2(x-5)}{3x}$

$\frac{2x-10}{x+16}=\frac{2x-10}{3x}$

$3x=x+16$

$2x=16$

x=8

Denominator = 8

Numerator = x-5=8-5=3

Fraction : $\frac{3}{8}$

Hence the original fraction is $\frac{3}{8}$