Select the fraction that will next in the following series.

2, 4, 6, 8, 10, 12, .....
3, 5, 7, 9, 11, 13, .....

The correct option is 14,15 (which represents the fraction 14/15).

To find the next fraction in the series, we can analyze the numerator and denominator sequences separately.

Step 1: Analyze the Numerator Sequence
The sequence of numerators is:
2, 4, 6, 8, 10, 12, ...
This is an arithmetic progression of even numbers starting from 2, where each subsequent number increases by 2:
2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
8 + 2 = 10
10 + 2 = 12
Therefore, the next term in the numerator sequence will be:
12 + 2 = 14

Step 2: Analyze the Denominator Sequence
The sequence of denominators is:
3, 5, 7, 9, 11, 13, ...
This is an arithmetic progression of odd numbers starting from 3, where each subsequent number increases by 2:
3 + 2 = 5
5 + 2 = 7
7 + 2 = 9
9 + 2 = 11
11 + 2 = 13
Therefore, the next term in the denominator sequence will be:
13 + 2 = 15

Conclusion:
Combining the next numerator (14) and the next denominator (15), the next fraction in the series is 14/15, which corresponds to the option 14,15.