Shortcut Techniques
Races and Games · Study material
Shortcut Techniques – Races and Games
Shortcut techniques in Races and Games help candidates solve speed-based and scoring-based aptitude questions quickly and accurately in SSC, Banking, Railway, Insurance, Defence, CAT, CDS, NDA, and various competitive examinations.
Most questions from this chapter are based on:
- Race Speed Ratios
- Lead and Lag Concepts
- Start or Handicap Problems
- Dead Heat Race
- Scoring Rate in Games
- Relative Speed
- Time Difference Problems
Learning shortcut methods reduces lengthy calculations and improves solving speed significantly.
Golden Formula of Races
Speed = Distance / Time
Shortcut #1: Race Ratio Formula
If A beats B by x metres in a race of y metres:
Speed Ratio = y : (y − x)
Example:
In a 100 m race, A beats B by 20 m.
Speed ratio:
100 : 80 = 5 : 4
✔ This is the most important shortcut in race problems.
Shortcut #2: Time Difference Shortcut
If A beats B by t seconds:
B’s Time = A’s Time + t
Useful for quickly finding race timings.
Shortcut #3: Same Distance Rule
When two persons cover the same distance:
Speed Ratio = Inverse Time Ratio
Example:
If speed ratio = 2 : 3
Then time ratio = 3 : 2
Shortcut #4: Start or Handicap Shortcut
If A gives B a start of x metres in a y metre race:
- A runs y metres.
- B runs (y − x) metres.
This concept is heavily used in aptitude exams.
Shortcut #5: Dead Heat Shortcut
In a dead heat race:
Time Taken by Both Players is Equal
Shortcut #6: Relative Speed Shortcut
When two runners move:
| Situation | Relative Speed |
|---|---|
| Same Direction | Difference of Speeds |
| Opposite Direction | Sum of Speeds |
Shortcut #7: Faster Runner Concept
The faster runner:
- Covers more distance in the same time.
- Takes less time for the same distance.
Shortcut #8: Speed Ratio from Remaining Distance
If A finishes a race and B is x metres behind in a race of y metres:
Speed Ratio = y : (y − x)
Very useful for direct MCQ solving.
Shortcut #9: Games Scoring Shortcut
In games:
Scoring Rate Ratio = Score Ratio
Example:
If A scores 100 while B scores 80:
Scoring ratio:
100 : 80 = 5 : 4
Shortcut #10: Point Handicap Shortcut
If A gives B x points in a game of y points:
- A scores y points.
- B scores (y − x) points.
Shortcut #11: Speed-Time Shortcut
When distance remains constant:
Speed ∝ 1 / Time
If speed doubles, time becomes half.
Shortcut #12: “x Times Faster” Concept
If A is x times faster than B:
A’s Speed = (1 + x) × B’s Speed
Example:
If A is 1/2 times faster than B:
A’s speed = 3/2 × B’s speed
Shortcut #13: Quick Distance Formula
Distance covered:
Distance = Speed × Time
Shortcut #14: Quick Time Formula
Time taken:
Time = Distance / Speed
Shortcut #15: Ratio Conversion Shortcut
If:
A : B = 5 : 4
Then:
- A covers 5 units when B covers 4 units.
- B lags by 1 unit.
Shortcut #16: Solving Race Questions Without Formula
Many MCQs can be solved using:
- Direct ratio observation
- Cross multiplication
- Proportional reasoning
Shortcut #17: Common Race Interpretation
In a 100 m race:
“A beats B by 20 m” means:
- A runs 100 m
- B runs only 80 m
Shortcut #18: Relative Performance Shortcut
In games:
- Points replace distance.
- Scoring rate replaces speed.
- Winning score replaces finishing point.
Shortcut #19: Quick Revision Formula Table
| Concept | Shortcut Formula |
|---|---|
| Speed | Distance / Time |
| Distance | Speed × Time |
| Time | Distance / Speed |
| Race Ratio | Total Distance : Remaining Distance |
| Relative Speed | Sum/Difference of Speeds |
| Scoring Ratio | Score Ratio |
| Dead Heat | Equal Time |
Shortcut #20: Most Important Exam Tricks
- Convert race problems into ratio problems.
- Use remaining-distance method directly.
- Memorize all basic formulas.
- Practice start and dead-heat questions regularly.
- Use scoring-rate concepts in game problems.
- Avoid lengthy calculations.
- Practice previous year aptitude questions.
Common Mistakes to Avoid
- Confusing speed ratio with time ratio.
- Ignoring remaining distance.
- Using incorrect race interpretation.
- Ignoring handicap/start conditions.
- Using wrong scoring ratios.
Important Exam Tips
- Memorize all race formulas thoroughly.
- Practice ratio-based questions daily.
- Improve calculation speed.
- Focus on logical interpretation.
- Use direct proportion methods.
- Practice game scoring problems regularly.
- Practice previous year aptitude questions.
Shortcut techniques in Races and Games help candidates improve calculation speed, logical analysis, and accuracy in solving competitive examination aptitude questions efficiently.