Races and Games of Skill

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Quantitative Aptitude Races and Games of Skill Competitive Exams

Races and Games of Skill is an important quantitative aptitude topic based on speed, distance, time, relative performance, starts, leads, dead heats, and advantage-based games. These questions are commonly asked in competitive exams, banking exams, railway exams, and aptitude tests.

What are Races and Games of Skill?

A race is a competition in which participants cover a fixed distance. The person who covers the distance first wins the race. Race problems compare the speeds and distances covered by different participants.

Games of skill are based on advantage, points, scores, or chances given to one player so that the game becomes fair or competitive. These questions usually involve leads, starts, winning margins, and required scores.

Quick idea: In race problems, compare the distance covered by each participant in the same time.

Term	Meaning	Example
Race	A competition to cover a fixed distance	100 m race
Lead	Distance by which a person is ahead	A beats B by 10 m
Start	Advantage given before the race begins	B gets a start of 20 m
Dead Heat	Both participants finish at the same time	A and B reach together
Game of Skill	Competition based on score or points	A gives B 10 points in a game of 100

“In race questions, the winner covers the full race distance while the loser covers less.”

Aptitude Tip

Key points

Winner covers the full race distance.
Loser covers less distance in the same time.
Lead means winning margin.
Start means initial advantage.
Dead heat means both finish together.
Compare speeds using distance ratio.

race lead start speed ratio dead heat

Visual Understanding

These diagrams show how lead, start, and finishing position are used in race problems.

A Beats B by 20 m in a 100 m Race

\[ A:B = 100:80 = 5:4 \]

If A beats B by 20 m in a 100 m race, then B covers only 80 m when A covers 100 m.

B Gets a Start of 20 m

\[ \text{Distance to be run by B}=100-20=80\text{ m} \]

A start means the weaker participant begins ahead of the normal starting point.

Dead Heat

\[ \text{Dead Heat} \Rightarrow \text{same finishing time} \]

In a dead heat, no participant wins because both finish together.

Game of 100 Points

\[ A:B = 100:90 = 10:9 \]

In games of skill, points or scores are compared like distances in races.

Important Formulas and Rules

Basic Speed Formula

\[ \text{Speed}=\frac{\text{Distance}}{\text{Time}} \]

Race problems are based on speed, distance, and time.

Speed Ratio

\[ S_A:S_B = D_A:D_B \]

When time is same, speed ratio equals distance ratio.

A Beats B by \(x\) m

\[ A:B = L:(L-x) \]

\(L\) is total race length.

B Gets Start of \(x\) m

\[ \text{Distance for B}=L-x \]

Start reduces the distance to be covered.

Winning Margin

\[ \text{Lead}=L-D_{\text{loser}} \]

Difference between finish line and loser’s position.

Time Ratio

\[ T_A:T_B=\frac{1}{S_A}:\frac{1}{S_B} \]

For same distance, time ratio is inverse of speed ratio.

Game of Points

\[ A:B=P:(P-x) \]

\(P\) is full score and \(x\) is points given.

Dead Heat

\[ T_A=T_B \]

Both participants finish at the same time.

Rule: If A beats B by \(x\) metres in a race of \(L\) metres, then when A covers \(L\) metres, B covers \(L-x\) metres.

Common Types of Questions

One Person Beats Another

Winner covers the full distance and loser covers less.

A beats B by 10 m
Find speed ratio
Find winning margin
Find equivalent start

Start Given

One participant starts ahead of the normal starting point.

Start in metres
Start in seconds
Equal race condition
Dead heat condition

Three Participants

Compare A with B, B with C, and then find A with C.

A beats B
B beats C
Find A beats C
Use speed ratios

Games of Skill

Scores or points are compared like race distances.

Game of 100
Points given
Score ratio
Winning margin

Exam approach: Convert every race statement into a distance ratio first. Then use the ratio to answer the question.

Method Bank

A Beats B by 20 m in 100 m

A covers 100 m, B covers 80 m.

\[ A:B=100:80=5:4 \]

B Gets 15 m Start in 100 m

B needs to cover only 85 m.

\[ 100-15=85 \]

Same Distance Race

Time ratio is inverse of speed ratio.

\[ T_A:T_B=\frac{1}{S_A}:\frac{1}{S_B} \]

Game of 100 Points

A gives B 20 points.

\[ A:B=100:80=5:4 \]

Tip: In races, “beats by” means the distance left for the loser when the winner finishes.

Race Solving Flow

Most race questions become easy after converting the information into distance ratio.

\[ \text{Winner distance}:\text{Loser distance} \]

\[ \text{Speed ratio}=\text{Distance ratio when time is same} \]

Step-by-Step Solving Method

Step	Race Problems	Games of Skill
Step 1	Identify the total race distance.	Identify the total points in the game.
Step 2	Identify who wins and by how much.	Identify how many points are given.
Step 3	Find loser’s covered distance.	Find weaker player’s effective score target.
Step 4	Convert distances into speed ratio.	Convert points into performance ratio.
Step 5	Use ratio to find required lead, start, or margin.	Use ratio to find points or advantage.

Important: In races, compare distances covered in the same time. In games of skill, compare points scored under the same condition.

Solved Examples

Question	Method	Answer
In a 100 m race, A beats B by 20 m. Find the ratio of speeds of A and B.	When A covers 100 m, B covers: \[ 100-20=80\text{ m} \] Since time is same: \[ A:B=100:80=5:4 \]	5 : 4
In a 200 m race, A beats B by 40 m. Find the speed ratio.	B covers: \[ 200-40=160\text{ m} \] Speed ratio: \[ A:B=200:160=5:4 \]	5 : 4
A and B run a 100 m race. A gives B a start of 20 m. How much distance does B need to run?	B starts 20 m ahead. \[ \text{Distance for B}=100-20=80\text{ m} \]	80 m
A can run 100 m while B can run 80 m in the same time. If the race is 200 m, by how much will A beat B?	Speed ratio: \[ A:B=100:80=5:4 \] When A covers 200 m, B covers: \[ 200\times\frac{4}{5}=160\text{ m} \] Lead: \[ 200-160=40\text{ m} \]	40 m
In a game of 100 points, A gives B 20 points. Find the performance ratio of A and B.	B needs to score: \[ 100-20=80 \] Performance ratio: \[ A:B=100:80=5:4 \]	5 : 4
A beats B by 10 m in a 100 m race. B beats C by 10 m in a 100 m race. By how much does A beat C?	A:B: \[ 100:90=10:9 \] B:C: \[ 100:90=10:9 \] Therefore: \[ A:C=100:81 \] When A covers 100 m, C covers 81 m.	A beats C by 19 m
A gives B 25 m start in a 100 m race and both finish together. Find speed ratio of A and B.	A runs 100 m, B runs: \[ 100-25=75\text{ m} \] Same time, so: \[ A:B=100:75=4:3 \]	4 : 3
In a game of 80 points, A gives B 16 points. Find the performance ratio.	B needs to score: \[ 80-16=64 \] Ratio: \[ A:B=80:64=5:4 \]	5 : 4

Note: In race problems, always convert the given winning margin into distance covered by the loser.

Common Traps and Shortcuts

Common Traps

Taking the lead as the loser’s covered distance.
Forgetting to subtract lead from total race distance.
Confusing start with winning margin.
Using time ratio instead of distance ratio when time is same.
Forgetting that points in games are treated like race distances.
Solving three-person races without converting into ratios.

Useful Shortcuts

A beats B by \(x\) m in \(L\) m race: use \(L:(L-x)\).
Start of \(x\) m means the person runs \(L-x\) m.
Same time means speed ratio equals distance ratio.
Same distance means time ratio is inverse of speed ratio.
Game of points works like race distance.
For A-B-C races, multiply ratios carefully.

Exam approach: First identify the total race length, then the actual distance covered by each participant.

Practice

A) Multiple Choice Questions

In a 100 m race, A beats B by 10 m. Find the speed ratio of A and B.
10 : 9 9 : 10 5 : 4 4 : 5
In a 200 m race, A beats B by 50 m. What distance does B cover when A finishes?
100 m 125 m 150 m 175 m
B gets a start of 20 m in a 100 m race. How much distance does B need to run?
60 m 70 m 80 m 90 m
In a game of 100 points, A gives B 25 points. Find A : B.
4 : 3 3 : 4 5 : 4 2 : 1
If A and B finish at the same time, the race is called:
Start Lead Dead heat Margin

B) Solve the Higher-Order Problems

In a 100 m race, A beats B by 20 m. Find the speed ratio of A and B. (Hint: B covers \(100-20\) m.)
In a 150 m race, A beats B by 30 m. Find the speed ratio. (Hint: Compare 150 m and 120 m.)
A can run 100 m while B runs 75 m. In a 200 m race, by how much will A beat B? (Hint: Use speed ratio \(100:75\).)
In a game of 120 points, A gives B 30 points. Find the ratio of skill of A and B. (Hint: B effectively scores \(120-30\).)
A beats B by 20 m in a 100 m race. B beats C by 20 m in a 100 m race. By how much does A beat C? (Hint: Use ratios \(100:80\) and \(100:80\).)

C) Match the Concept with the Correct Meaning

Concept	Correct Meaning
Lead	Distance by which the winner is ahead
Start	Initial advantage given before the race begins
Dead Heat	Both participants finish together
Speed Ratio	Ratio of distances covered in the same time
Game of Skill	Competition based on points or scores
Winning Margin	Difference between finish line and loser’s position

Aptitude Reminder

Races and games of skill are solved by comparing performance. In races, compare distances. In games, compare points. Always subtract the lead or start from the total distance or score.

Task: Create five questions using lead, start, dead heat, three-person race, and game of points.

Show Suggested Answers

Multiple Choice

10 : 9
B covers:
\[ 100-10=90\text{ m} \]

\[ A:B=100:90=10:9 \]
150 m

\[ 200-50=150\text{ m} \]
80 m

\[ 100-20=80\text{ m} \]
4 : 3
B effectively scores:
\[ 100-25=75 \]

\[ A:B=100:75=4:3 \]
Dead heat
When both participants finish at the same time, it is called a dead heat.

Higher-Order Problems

In a 100 m race, A beats B by 20 m.
\[ B=100-20=80\text{ m} \]

\[ A:B=100:80=5:4 \]
Answer = 5 : 4.
In a 150 m race, A beats B by 30 m.
\[ B=150-30=120\text{ m} \]

\[ A:B=150:120=5:4 \]
Answer = 5 : 4.
A:B speed ratio:
\[ 100:75=4:3 \]
When A runs 200 m, B runs:
\[ 200\times\frac{3}{4}=150\text{ m} \]
Lead:
\[ 200-150=50\text{ m} \]
Answer = 50 m.
In a game of 120 points, A gives B 30 points.
\[ B=120-30=90 \]

\[ A:B=120:90=4:3 \]
Answer = 4 : 3.
A beats B by 20 m:
\[ A:B=100:80=5:4 \]
B beats C by 20 m:
\[ B:C=100:80=5:4 \]
Therefore:
\[ A:C=25:16 \]
When A covers 100 m, C covers:
\[ 100\times\frac{16}{25}=64\text{ m} \]
Lead:
\[ 100-64=36\text{ m} \]
Answer = A beats C by 36 m.

Concept Matching

Lead → Distance by which the winner is ahead
Start → Initial advantage given before the race begins
Dead Heat → Both participants finish together
Speed Ratio → Ratio of distances covered in the same time
Game of Skill → Competition based on points or scores
Winning Margin → Difference between finish line and loser’s position

Clue Explanation

In races, the winner covers the full distance. The loser’s covered distance is found by subtracting the winning margin from the total race distance. This gives the speed ratio.

Exam tips

Winner always covers full race distance.
Loser’s distance = race length minus lead.
Start reduces the distance to be covered.
Same time means distance ratio equals speed ratio.
Same distance means time ratio is inverse of speed ratio.
Games of skill use points like race distance.

Practice MCQs

Learning Modules