Races and Games Questions for Placement (with Solutions)

Last Updated: March 2026

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

Companies Testing This Topic

Company	Frequency	Difficulty
TCS	Sometimes	Easy-Medium
Infosys	Sometimes	Easy
Wipro	Rare	Medium
Cognizant	Sometimes	Easy
Accenture	Rare	Medium
Capgemini	Sometimes	Easy

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.

Master the ratio concept and Races and Games becomes easy!

Races And Games Questions Placement