In a 10 km marathon race, A beats B by 1000 meters, and B beats C by 1250 meters. By how many meters does A beat C in the same ra…

Question

In a 10 km marathon race, A beats B by 1000 meters, and B beats C by 1250 meters. By how many meters does A beat C in the same race?

1. A. 2125 m (Correct answer)
2. B. 1250 m
3. C. 2250 m
4. D. 2150 m

Correct Answer

Option A — 2125 m

Detailed Solution & Explanation

The correct answer is 2125 m.

Key Points

• In a 10,000 m race, when A finishes, B has covered 10,000 − 1,000 = 9,000 m.
• Separately, when B finishes 10,000 m, C has covered 10,000 − 1,250 = 8,750 m, so C runs at 8,750/10,000 = 0.875 times B's speed.
• At the moment A finishes, B is at 9,000 m, so C is at 9,000 × 0.875 = 7,875 m.
• A therefore beats C by 10,000 − 7,875 = 2,125 m.

Additional Information

• The two 'beats by' figures cannot simply be added: 1,000 + 1,250 = 2,250 is the distractor, and it is wrong because C's shortfall must be scaled to the distance B has actually run.
• The reliable method is to convert each lead into a speed ratio and then combine the ratios.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*