Races and Games
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Solved Examples
Study MaterialSolved Examples – Races and Games
Solved examples help students understand the practical application of speed, distance, ratios, relative speed, scoring rate, and race concepts in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, Insurance, Defence, CAT, CDS, NDA, and various aptitude examinations.
Topics Covered in Solved Examples
- Race Ratio Problems
- Lead and Lag Concepts
- Relative Speed Questions
- Start or Handicap Problems
- Dead Heat Race
- Scoring Rate in Games
- Time Difference Problems
- Advanced Race Applications
Example 1: Basic Race Problem
Question: In a 100 m race, A beats B by 20 m. Find the ratio of their speeds.
Solution:
When A finishes 100 m, B covers only 80 m.
Speed ratio:
A : B = 100 : 80
= 5 : 4
Answer: 5 : 4
Example 2: Finding Remaining Distance
Question: In a 200 m race, A beats B by 40 m. How much distance does B cover when A finishes the race?
Solution:
A finishes 200 m.
B is 40 m behind.
Distance covered by B:
= 200 − 40
= 160 m
Answer: 160 m
Example 3: Time Difference Problem
Question: A can run 100 m in 10 seconds and B can run 100 m in 12 seconds. By how many seconds does A beat B?
Solution:
Time taken by A = 10 seconds
Time taken by B = 12 seconds
Difference:
= 12 − 10
= 2 seconds
Answer: 2 seconds
Example 4: Relative Speed Problem
Question: Two runners run at 12 km/hr and 8 km/hr in the same direction. Find their relative speed.
Solution:
Relative speed in same direction:
= Difference of speeds
= 12 − 8
= 4 km/hr
Answer: 4 km/hr
Example 5: Opposite Direction Race
Question: Two runners move at 10 km/hr and 15 km/hr in opposite directions. Find their relative speed.
Solution:
Relative speed in opposite direction:
= Sum of speeds
= 10 + 15
= 25 km/hr
Answer: 25 km/hr
Example 6: Start or Handicap Problem
Question: In a 100 m race, A can give B a start of 20 m. Find the ratio of their speeds.
Solution:
A runs 100 m.
B runs only 80 m.
Speed ratio:
= 100 : 80
= 5 : 4
Answer: 5 : 4
Example 7: Dead Heat Race
Question: Two runners finish a race together. What is the ratio of their times?
Solution:
In a dead heat:
Time taken by both runners is equal.
Time ratio:
= 1 : 1
Answer: 1 : 1
Example 8: Game Scoring Problem
Question: In a game of 100 points, A scores 100 while B scores 80. Find the ratio of their scoring rates.
Solution:
Scoring rate ratio:
= 100 : 80
= 5 : 4
Answer: 5 : 4
Example 9: Distance Covered Problem
Question: A and B run in the ratio 3 : 2. If A covers 300 m, how much distance does B cover in the same time?
Solution:
Speed ratio:
A : B = 3 : 2
If A covers 300 m:
B covers:
= (2/3) × 300
= 200 m
Answer: 200 m
Example 10: Time Ratio Problem
Question: A and B can complete the same race in the ratio 4 : 5. Find the ratio of their speeds.
Solution:
Speed ratio is inverse of time ratio.
Speed ratio:
= 5 : 4
Answer: 5 : 4
Example 11: “x Times Faster” Problem
Question: A is 50% faster than B. Find the ratio of their speeds.
Solution:
50% faster means:
A’s speed = 150% of B’s speed
Ratio:
= 150 : 100
= 3 : 2
Answer: 3 : 2
Example 12: Advanced Race Problem
Question: In a 500 m race, A beats B by 50 m and C by 100 m. Find the ratio of the speeds of B and C.
Solution:
When A runs 500 m:
B runs 450 m
C runs 400 m
Speed ratio:
B : C = 450 : 400
= 9 : 8
Answer: 9 : 8
Example 13: Game Handicap Problem
Question: In a game of 80 points, A gives B a start of 20 points. Find the ratio of their scoring rates.
Solution:
A scores 80 points.
B scores only:
= 80 − 20
= 60 points
Scoring ratio:
= 80 : 60
= 4 : 3
Answer: 4 : 3
Example 14: Speed and Time Problem
Question: A runs twice as fast as B. If B takes 30 seconds to complete a race, how much time does A take?
Solution:
If speed doubles, time becomes half.
Time taken by A:
= 30/2
= 15 seconds
Answer: 15 seconds
Example 15: Combined Race Concept
Question: A beats B by 20 m in a 100 m race. B beats C by 10 m in a 100 m race. By how many metres does A beat C?
Solution:
A : B = 100 : 80
= 5 : 4
B : C = 100 : 90
= 10 : 9
Therefore:
A : C = (5/4) × (10/9)
= 25 : 18
When A runs 100 m:
C runs:
= (18/25) × 100
= 72 m
A beats C by:
= 100 − 72
= 28 m
Answer: 28 m
Important Exam Tips
- Convert race questions into ratio problems.
- Memorize all important formulas thoroughly.
- Use direct proportion methods wherever possible.
- Practice handicap and dead-heat problems regularly.
- Understand relative speed carefully.
- Improve simplification speed.
- Practice previous year aptitude questions.
Common Mistakes to Avoid
- Confusing speed ratio and time ratio.
- Ignoring remaining distance.
- Using incorrect race interpretation.
- Ignoring handicap conditions.
- Using wrong scoring relationships.
Practicing solved examples regularly improves conceptual clarity, logical thinking ability, and calculation speed in solving Races and Games aptitude questions in competitive examinations.