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Why Race Questions Look Harder Than They Are
Race and track questions come wrapped in stories: A beats B by 10 metres, C gives D a head start, two athletes run around a stadium. Underneath, every one of them is the speed-time-distance formula applied to two people at once.
Two habits solve almost everything. First, in a race, both runners run for the same time, so the distances they cover in that time are in the same ratio as their speeds. Second, on a circular track, the question is always about how much one runner gains on the other, and the gain needed is exactly one full lap (or the track length once, for opposite directions).
This short builds both habits with the formulas and worked examples that Railway, SSC and TRE-4 mental-maths sections reuse year after year.
1. In a 100 m race, A beats B by 10 m. What is the ratio of the speeds of A and B?
2. In a 1000 m race A beats B by 100 m, and in another 1000 m race B beats C by 100 m. By how many metres does A beat C in a 1000 m race?
3. Two runners start together from the same point of a 600 m circular track in the same direction at 8 m/s and 4 m/s. After how much time do they meet for the first time?
4. Two runners start from the same point of a 360 m circular track in opposite directions at 7 m/s and 5 m/s. After how many seconds do they meet for the first time?
5. A takes 24 s and B takes 36 s to complete one lap. They start together from the starting line in the same direction. After how many seconds will they be together at the starting line again?
6. A runs 100 m in 20 s and B runs 100 m in 25 s. In a 100 m race, by how many metres does A beat B?
7. In a 1 km race A beats B by 10 seconds, and A finishes in 90 seconds. By how many metres does A beat B?
8. Two persons start from the same point of a 400 m circular track in opposite directions at 3 m/s and 5 m/s. How many times do they meet in 200 seconds?