The numerator of a fraction is less than its denominator by 2. If we subtract 2 from the numerator and add 2 to the denominator, then the new fraction is $$\frac{1}{3}$$. What is the original fraction?

Correct option is D

Given:

Numerator of a fraction is 2 less than the denominator

If 2 is subtracted from numerator and 2 is added to denominator then fraction will be $$\frac{1}{3}$$​​

Solution:

Let the denominator be x

Then numerator will be x -2

According to question:

​$$\frac{x-2 -2}{x +2 } =\frac{1}{3}$$​​

​$$\frac{x-4}{x+2} =\frac{1}{3}$$​​

3(x - 4) = x + 2

3x- 12 = x + 2

2x = 14

x = 7

Then denominator is 7

The numerator is x -2 = 5

The original fraction is = $$\frac{5}{7}$$​​