Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.
8:14::13:24::9:?

Let's look at the mathematical relation between the pairs of numbers:
For the first pair: 8×2−2=16−2=14

For the second pair: 13×2−2=26−2=24

Following this uniform pattern (x×2−2) for the third pair:

9×2−2=18−2=16

Thus, the required number is 16.