The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator, the fraction would become 2/3. Find the fraction?

15/31

3/14

9/14

None of these

Let's denote the denominator as x. Then, the numerator is x - 5.

Original fraction: (x - 5)/x

After adding 1 to both numerator and denominator:

New fraction: (x - 5 + 1)/(x + 1) = (x - 4)/(x + 1)

Given that the new fraction is 2/3:

(x - 4)/(x + 1) = 2/3

Cross-multiply:

3(x - 4) = 2(x + 1)

Expand and solve:

3x - 12 = 2x + 2

x = 14

So, the original fraction is:

(x - 5)/x = (14 - 5)/14 = 9/14