Question

The denominator of a fraction exceeds numerator by 3. If one is added to both numerator and denominator, the difference between the new and the original fractions is 1/24. Find the original fraction.

Answer 1

Given data:

Let the Numerator is N

Denominator = N+3

Original fraction = N/(N+3)

Adding 1 to Numerator and denominator gives the new fraction = (N+1) / (N+4)

Difference of both fraction = 1/24

Solution:

{(N+1) / (N+4)} – {N/(N+3)} = 1/24

On solving the equation,

24{(N+1)(N+3) – N(N+4)} = (N+4) ( N+3)

24 {N^2 + 4N+3 – N^2-4)} = N^2+7N-12

24 x 3 = N^2+7N-12

= > N^2+7N-60 = 0

This can also be written as:

N(N+12)-5(N+12) = 0

= > (N+12) (N-5) = 0

If we consider N+12 = 0, N will be equal to -12 but N has to be a positive number.

So N-5=0

Thus Numerator = 5

Denominator = N+3 = 8

Original fraction = 5/8