Question

The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5 . find the original number

Answer 1

5/8

Explanation:

Let the numerator = n.

Let the denominator = d.

The fraction is

n/d

"The denominator of a rational number is greater than its numerator by 3."

d = n + 3

The fraction is

n/(n + 3)

"If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5."

(n - 3)/(n + 3 + 2) = 1/5

(n - 3)/(n + 5) = 1/5

Cross multiply.

5(n - 3) = 1(n + 5)

5n - 15 = n + 5

4n = 20

n = 5

d = n + 3 = 5 + 3 = 8

n/d = 5/8

The original number is 5/8.