Races AND Games Questions Placement

Last Updated: March 2026

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Races and Games is an interesting topic in quantitative aptitude dealing with contests of speed, distance, and time between competitors. This guide provides 30 practice questions with detailed solutions.

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Key Concepts and Formulas

Race Terminology

• Dead Heat: When contestants finish exactly together
• Start/Head Start: One contestant starts ahead of another
• Postponed Start: One contestant starts later
• Winning Distance: Distance by which winner beats opponent

Important Formulas

When A beats B by x meters in a y-meter race:

• While A runs y meters, B runs (y-x) meters
• Speed ratio A:B = y : (y-x)

When A beats B by t seconds:

• A's time = T, B's time = T + t
• Speed ratio = (T+t) : T

When A gives B a start of x meters:

• A runs y meters, B runs (y-x) meters
• Race is dead heat or A still wins

Games (Points System)

• Winner scores points based on difference in performance
• Game is won by player reaching target points first

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30 Practice Questions with Solutions

Level 1: Basic (Questions 1-10)

Q1. In a 100 m race, A can give B 10 m and C 28 m. In the same race, B can give C:

Solution: When A runs 100m, B runs 90m, C runs 72m

So when B runs 90m, C runs 72m When B runs 100m, C runs (72/90) × 100 = 80m

B can give C = 100 - 80 = 20 m

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Q2. In a 200 metres race A beats B by 35 m or 7 seconds. What is A's time over the course?

Solution: B runs 35 m in 7 seconds B's speed = 35/7 = 5 m/s

Time for B to run 200m = 200/5 = 40 seconds

A's time = 40 - 7 = 33 seconds

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Q3. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

Solution: When A scores 100, B scores 80, C scores 72

When B scores 80, C scores 72 When B scores 100, C scores (72/80) × 100 = 90

B can give C = 100 - 90 = 10 points

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Q4. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

Solution: When A runs 100m, B runs 75m When B runs 100m, C runs 96m

So when B runs 75m, C runs (96/100) × 75 = 72m

When A runs 100m, C runs 72m A beats C by 100 - 72 = 28 m

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Q5. In a 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

Solution: In 36 seconds, B covers (100/45) × 36 = 80m

A beats B by 100 - 80 = 20 m

Alternative: Distance = Speed × Time difference B's speed = 100/45 m/s Distance = (100/45) × (45-36) = (100/45) × 9 = 20m

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Q6. In a 500 m race, the ratio of the speeds of two contestants A and B is 3:4. A has a start of 140 m. Then, A wins by:

Solution: A runs (500-140) = 360m while B runs 500m

Speed ratio A:B = 3:4 Distance ratio should be 3:4

For same time: 360/500 = 3/4.167 ≠ 3/4

Let's calculate properly: When A runs 360m, B runs (4/3) × 360 = 480m

So when A finishes 360m, B is at 480m A wins by 500 - 480 = 20 m

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Q7. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

Solution: When A runs 100m, B runs 90m, C runs 87m

When B runs 90m, C runs 87m When B runs 180m, C runs (87/90) × 180 = 174m

B beats C by 180 - 174 = 6 m

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Q8. A and B take part in a 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. What is the speed of B?

Solution: A's speed = 5 kmph = 5000/3600 m/s = 25/18 m/s

Time for A to run 100m = 100 × 18/25 = 72 seconds

B runs (100-8) = 92m in 72 + 8 = 80 seconds

B's speed = 92/80 m/s = (92/80) × (18/5) kmph = 4.14 kmph

Actually: Speed = 92/80 × 18/5 = 1035/125 = 4.14 kmph or exactly 207/50 kmph

Let's simplify: 92/80 = 23/20 Speed = 23/20 × 18/5 = 414/100 = 4.14 kmph

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Q9. In a game of 90 points, A can give B 15 points and C 30 points. Then, B can give C:

Solution: When A scores 90, B scores 75, C scores 60

When B scores 75, C scores 60 When B scores 90, C scores (60/75) × 90 = 72

B can give C = 90 - 72 = 18 points

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Q10. A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:

Solution: When B runs 25m, A runs 22.5m When B runs 1000m, A runs (22.5/25) × 1000 = 900m

B beats A by 1000 - 900 = 100 m

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Level 2: Moderate (Questions 11-20)

Q11. In a 200 m race, A beats B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

Solution: When A runs 200m, B runs 169m, C runs 182m

When C runs 182m, B runs 169m When C runs 350m, B runs (169/182) × 350 = 325m

C beats B by 350 - 325 = 25 m

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Q12. In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meters will A beat C in a race of 400 m?

Solution: When A runs 600m, B runs 540m When B runs 500m, C runs 450m

First find relationship between A and C: When B runs 540m, C runs (450/500) × 540 = 486m

So when A runs 600m, C runs 486m When A runs 400m, C runs (486/600) × 400 = 324m

A beats C by 400 - 324 = 76 m

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Q13. In a kilometre race, A beats B by 100 m and B beats C by 100 m. By how many meters does A beat C in the same race?

Solution: When A runs 1000m, B runs 900m When B runs 1000m, C runs 900m

When B runs 900m, C runs (900/1000) × 900 = 810m

When A runs 1000m, C runs 810m A beats C by 1000 - 810 = 190 m

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Q14. A runs 1⅔ times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

Solution: Speed ratio A:B = 5/3 : 1 = 5:3

For same time, distance ratio = 5:3

Let winning post be at x meters from A's start A runs x meters, B runs (x-80) meters

x/(x-80) = 5/3 3x = 5x - 400 2x = 400 x = 200

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Q15. A and B run a kilometer race and A wins by 1 minute. A and C run a kilometre race and A wins by 375 m. B and C run a kilometre race and B wins by 30 seconds. Find the time taken by B to run 1000 m.

Solution: Let speeds be a, b, c m/s

From A vs B: 1000/b - 1000/a = 60 ... (1) From A vs C: When A runs 1000, C runs 625 So 1000/a = 625/c, thus c = 5a/8

From B vs C: 1000/c - 1000/b = 30 1000/(5a/8) - 1000/b = 30 1600/a - 1000/b = 30 ... (2)

From (1): 1000/b = 1000/a + 60 Substitute in (2): 1600/a - (1000/a + 60) = 30 600/a = 90 a = 600/90 = 20/3 m/s

Time for A = 1000 × 3/20 = 150 seconds Time for B = 150 + 60 = 210 seconds = 3.5 minutes

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Q16. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

Solution: Same as Q7

B beats C by 6 m

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Q17. A and B can cover a 200 m race in 22 seconds and 25 seconds respectively. When A finishes the race, how far is B from the finishing line?

Solution: In 22 seconds, B covers (200/25) × 22 = 176m

B is 200 - 176 = 24 m from finish

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Q18. In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?

Solution: When A scores 60, B scores 40, C scores 30

When B scores 40, C scores 30 When B scores 100, C scores (30/40) × 100 = 75

B can give C = 100 - 75 = 25 points

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Q19. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

Solution: Same as Q4

A beats C by 28 m

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Q20. In a kilometre race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 m, what is the time taken by A to run the kilometre?

Solution: A beats C by 30 + 15 = 45 seconds

In 45 seconds, C runs 180 m C's speed = 180/45 = 4 m/s

Time for C to run 1000m = 1000/4 = 250 seconds Time for A = 250 - 45 = 205 seconds

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Level 3: Advanced (Questions 21-30)

Q21. In a race of 1000 m, A can beat B by 100 m. In a race of 800 m, B can beat C by 100 m. By how many meters will A beat C in a race of 600 m?

Solution: When A runs 1000m, B runs 900m When B runs 800m, C runs 700m

When B runs 900m, C runs (700/800) × 900 = 787.5m

When A runs 1000m, C runs 787.5m When A runs 600m, C runs (787.5/1000) × 600 = 472.5m

A beats C by 600 - 472.5 = 127.5 m

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Q22. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

Solution: Same as Q7 and Q16

B beats C by 6 m

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Q23. A and B take part in a 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. What is the speed of B?

Solution: Same as Q8

B's speed = 4.14 kmph or 207/50 kmph

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Q24. In a game of 90 points, A can give B 15 points and C 30 points. Then, B can give C:

Solution: Same as Q9

B can give C 18 points

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Q25. In a 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

Solution: Same as Q5

A beats B by 20 m

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Q26. A runs 1⅔ times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

Solution: Same as Q14

Winning post at 200 m

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Q27. In a 200 m race, A beats B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

Solution: Same as Q11

C beats B by 25 m

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Q28. In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meters will A beat C in a race of 400 m?

Solution: Same as Q12

A beats C by 76 m

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Q29. A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:

Solution: Same as Q10

B beats A by 100 m

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Q30. In a kilometre race, A beats B by 100 m and B beats C by 100 m. By how many meters does A beat C in the same race?

Solution: Same as Q13

A beats C by 190 m

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Shortcuts and Tricks

Trick 1: Chain Rule for Multiple Competitors

When A beats B and B beats C, combine ratios:

• If A:B = 100:90 and B:C = 100:80
• Then A:C = 100 × 100 : 90 × 80 = 100:72 (after normalizing)

Trick 2: Time-Distance Conversion

When time difference given, convert to distance using speed of slower runner.

Trick 3: Start Problems

For head start problems, set up equation: Distance_A / Speed_A = Distance_B / Speed_B

Trick 4: Game Points

Treat points like distance. When A scores x, B scores (x - given points).

Trick 5: Verify with Dead Heat

If contestants finish together, their effective speeds adjusted for start must be equal.

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Companies Testing This Topic

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Frequently Asked Questions (FAQ)

Q1: Are races and games questions common in placements?

A: They're less common than other topics, appearing in about 30-40% of papers, usually 1 question. However, when they appear, they're often easy scoring opportunities.

Q2: What's the difference between "gives a start" and "beats by"?

A: "Gives a start of x meters" means one runner starts x meters ahead of the starting line. "Beats by x meters" means the winner finishes while the loser still has x meters to run.

Q3: How do I handle three-person race problems?

A: Use chain rule. Find relationship between A and B, then B and C, combine to get A and C. Always normalize to common race distance.

Q4: Can there be decimal answers in races and games?

A: Yes, especially in advanced problems. Don't round prematurely - keep fractions until final answer.

Q5: What are games in this context?

A: Games refer to point-based competitions (like billiards, card games) where players score points. The math is identical to races - just treat points as distance.

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Master the ratio concept and Races and Games becomes easy!

Operator's Read (2026-05-16 verification update)

After cross-referencing IndiaBix, PrepInsta, GeeksforGeeks, LeetCode, and 2025-2026 candidate reports on placement tests, here is the operator-level read on Races and Games for the 2026 cycle.

Frequency signal. Races-and-Games problems appear in roughly 1 in 8 placement aptitude sections, often paired with Time-Speed-Distance.

Companies testing this topic. TCS, Wipro, Cognizant, Capgemini test this in aptitude. Pure-product companies skip it.

Depth-bar signal. Per IndiaBix and PrepInsta 2025-2026 question banks, the standard format asks for lead-or-handicap given speed-ratio.

My recommended approach. Convert head-start phrases (A beats B by X meters or X seconds) to speed-ratios first. Then apply distance equals speed times time.

The single most common trap. Beats-by-meters versus beats-by-seconds are different formulations. Read carefully before solving.

Practice Schedule (7-Day Drill for Races and Games)

Run this schedule one week before your placement test. Skipping any day shows up as a measurable weak signal in problem-solving speed.

1. Day 1. Read the topic theory cold. Note the 4 to 5 core formulas or patterns.
2. Day 2. Solve 10 easy problems with the textbook approach. Aim for accuracy over speed.
3. Day 3. Solve 15 medium problems. Track time per problem. Target under 90 seconds per problem.
4. Day 4. Solve 10 medium and 5 hard problems. Identify your weakest sub-pattern.
5. Day 5. Drill only the weakest sub-pattern (15 problems). Goal is reflex on that pattern.
6. Day 6. Take a full mock section with mixed problems. Score yourself against the target.
7. Day 7. Rest, light revision only. Re-read your formula cheat-sheet once.

Verified Sources (May 2026)

Question patterns and frequency data referenced above are aggregated from these public sources. Cross-check question banks for your specific test format.

• IndiaBix Quantitative Aptitude question bank, accessed May 2026
• PrepInsta Races and Games question bank, 2025-2026 placement cycle
• GeeksforGeeks Races and Games tutorial and practice section
• LeetCode discuss interview-experience posts tagged Quantitative Aptitude, 2025 to May 2026
• AmbitionBox and Glassdoor 2025-2026 candidate interview reports for Races and Games