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.
Answers
Answered by
2
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
Similar questions