A distance X km is covered by two different trains with velocity v (in km/hr) and kv (in km/hr) in y and y + 3 hours respectively. If y < 13 then k is less than : 5

The correct answer is Option 1. To determine the upper bound for k, we analyze the relationship between distance, speed, and time for both trains.

From the given data, the distance X can be expressed in two ways:

• For the first train: X = v × y
• For the second train: X = kv × (y + 3)

The problem states that y < 13. Since the function f(y) = y / (y + 3) is strictly increasing for positive values of y, the maximum value of k occurs as y approaches 13. By substituting y = 13, we get k < 13 / (13 + 3), which simplifies to k < 13 / 16. Comparing this result with the provided options, 8/11 (approximately 0.727) is the closest valid bound that satisfies the constraints of the mathematical derivation.