Explanation:

- Train X and train Y both start from the same station A simultaneously.

- Train X reduces its speed by 25% after 60 km, while train Y does so after 90 km.

- Train X reaches station B at 10 AM, while train Y reaches at 9:45 AM.

- If both had traveled at their original speeds, they would reach station B at 8:30 AM.

- This implies both trains travel slower after their respective slowing-down points.

- To find the time ratio for half the distance, consider half of the original journey.

- Calculate using the proportions of their speed changes and distances where they maintain original speed versus reduced speed.

The correct option for the time ratio to cover half the distance AB is:

14 : 13.

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