In this question, we are given that two trains cover a distance of X km. The first train has a velocity of v km/hr and takes y hours to cover the distance. The second train has a velocity of kv km/hr and takes y + 3 hours to cover the same distance.

To solve the problem, we need to find the value of k under the condition y < 13.

Let`s analyze the options:

Option 1: k = 8 is not a valid option because there is no relation between y and k.

Option 2: k = 16 is a possibility. We cannot determine if it is the correct answer without analyzing the other options.

Option 3: k = 4 is not correct because it is less than 5.

Option 4: k = 16 is also a possibility. We cannot determine if it is the correct answer without analyzing the other options.

To determine the correct answer, we need to consider the condition y < 13. Since none of the options provide any relation between y and k, we can conclude that the correct answer cannot be determined based on the information given.

Therefore, the correct answer should be "Cannot be determined" or "Insufficient information provided."

Alert - correct answer should be "Cannot