Races And Games- Quantitative Aptitude Practice Question & Answer

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Preparing for a test with math questions about races and games? This subject is often seen in quantitative aptitude tests and entrance exams.

It requires important ideas and examples often seen in tests. Knowing the main terms and formulas used in these problems can help you do better on exams.

Important Concept In Races And Games

Let us study some of the important concepts in races and games:

In a race, when A gives B a head start of x meters, it means that both A and B are in the same race, but B gets to begin x meters ahead. As a result, while A has to cover the entire distance from start to finish, B only needs to run the remaining distance after their head start.

In a race, when A beats B by x meters, it indicates that A finishes ahead of B by a distance of x meters.

In a race, A can offer B a head start of “t” minutes. This means that although they both start at different times, they will reach the finish line simultaneously.

In a race scenario, when A is given a head start of x meters over B, it indicates that both A and B kick off the race simultaneously. However, B finishes the race t minutes after A completes it.

A dead heat happens when two or more racers cross the finish line simultaneously, resulting in a tie with no definite winner.

In races and games, a handicap is a way to make things fair by giving some participants a head start or other advantage. This helps to even the playing field, especially when there's a big difference in skill or experience levels among the players.

Calculating Time, Speed & Distance

When calculating time, speed, and distance, it's important to understand the relationship between these variables. Time is the duration it takes to cover a certain distance at a given speed.

Speed is the rate at which an object travels over a specific distance in a set amount of time. Distance is the total length or space between two points.

Formula

Knowing the speed, distance, or time allows you to accurately figure out any of the other variables. This is particularly handy in sports and races, where timing and distance play a key role in deciding results.

Time = Distance/Speed

Speed = Distance/Time

Distance = Speed x Time

Importance Of Races And Games Problems

Let us study the importance of races and games problems:

Enhancing Aptitude

Practicing race problems is crucial for honing quantitative aptitude skills, and fostering quick thinking and mental agility. It enhances logical reasoning, promoting strategic approaches to problem-solving through systematic analysis and critical thinking.

Competitive Exams

In competitive exams, solving race problems showcases an individual's ability to manage time efficiently while maintaining accuracy. Competence in race problems can significantly boost one's performance in various entrance exams.

Sample Practice Questions With Answers

Question 1:Consider a race where A and B start from points 100m and 150m respectively. If A covers 10m in every stride, while B covers 15m, when will B overtake A?

A) B will overtake A at the starting point.
B) B will overtake A after 5 strides.
C) B will overtake A after 10 strides.
D) B will overtake A after 15 strides.

Answer: C) B will overtake A after 10 strides.

Explanation: To find out when B will catch up to A, we calculate how many steps each runner needs to cover the gap. B starts 50m ahead of A. A takes 10m steps while B takes 15m steps, closing the gap by 5m with each step. So, B will need 10 steps to cover the initial 50m gap.

Question 2: In a 200-meter race, runner A starts from the starting line while runner B starts from a point 20 meters behind the starting line. If runner A runs at a constant speed of 8 meters per second and runner B runs at a constant speed of 10 meters per second, when will runner B overtake runner A?

A) B will overtake A immediately after the start.
B) B will overtake A after 2 seconds.
C) B will overtake A after 4 seconds.
D) B will overtake A after 10 seconds.

Answer: D) B will overtake A after 10 seconds.

Explanation: Runner B starts 20 meters behind Runner A. Runner A runs at 8 meters per second, and Runner B runs at 10 meters per second. So, it will take Runner B 10 seconds to catch up with Runner A for the initial 20-meter gap.

Question 3: In a race of 200 m, A can beat B by 28 m and C by 15 m. If C and B run a race of 350 m, by how many meters will C beat B?

A) 26 m
B) 32 m
C) 38 m
D) 44 m

Answer: B) 32 m

Explanation: In a 200-meter race, C is 18 meters behind B. So, C's speed relative to B is 18/200 meters per meter. In a 350-meter race, C will beat B by 18/200×350=31.5 meters approximately. So, the correct answer is 32 meters.

Question 4: In a 400-meter race, A beats B by 60 meters. If B covers 500 meters in 80 seconds, how long will A take to cover the same distance?

A) 72 seconds
B) 80 seconds
C) 90 seconds
D) 78 seconds

Answer: D) 78 seconds

Explanation: In a 400-meter race, A beats B by 60 meters. B runs 500 meters in 80 seconds. B's speed is 6.25 m/s. A's speed is 0.15 m/s faster than B's. A's speed is 6.4 m/s. To cover 500 meters, A takes around 78 seconds.

Question 5: A and B take part in a 150 m race. A runs at 6 km per hour. A gives B a start of 10 m and still beats him by 10 seconds. What is the speed of B?

A) 4 km/h
B) 5 km/h
C) 6 km/h
D) 7 km/h

Answer: A) 4 km/h

Explanation: A runs at 6 km/h and gives B a 10-meter head start. In a 150 m race, A beats B by 10 seconds. To find B's speed, we calculate that B's speed is 1.6 m/s or 4 km/h.

Question 6: In a 400-meter race, A beats B by 20 seconds. If B covers 500 meters in 100 seconds, how long will A take to cover the same distance?

A) 80 seconds
B) 60 seconds
C) 100 seconds
D) 110 seconds

Answer: B) 60 seconds

Explanation: The question is about a race where A beats B by 20 seconds in a 400-meter race. If B covers 500 meters in 100 seconds, we can calculate B's speed as 5 meters per second. A will take 60 seconds to cover the same 400 meters, considering the 20-second lead over B.

Question 7: In a 300-meter race, A beats B by 15 seconds. If B covers 400 meters in 80 seconds, how long will A take to cover the same distance?

A) 60 seconds
B) 70 seconds
C) 75.86 seconds
D) 86.78 seconds

Answer: D) 86.78 seconds

Explanation: To figure out how long A will take to cover the same distance as B, first find B's speed. B covers 400 meters in 80 seconds, so B's speed is 5 meters per second.

Since A beats B by 15 seconds in a 300-meter race, calculate A's speed. A's speed is 4.615 meters per second. To cover 400 meters, A will take around 86.78 seconds, just a bit more than a minute and a half.

Question 8: A and B are participating in a race. If A covers a distance of 300 meters in 45 seconds and B covers the same distance in 60 seconds, by how many meters does A beat B?

A) 95 meters
B) 89 meters
C) 100 meters
D) 80 meters

Answer: C) 100 meters

Explanation: A finishes 300 meters in 45 seconds, while B takes 60 seconds. The time difference is 15 seconds. A's speed is 6.67 meters per second. In 15 seconds, B covers 100 meters less than A. So, A beats B by running 100 meters farther in the same time.

Question 9: A car travels 240 kilometres in 3 hours. What is its speed in kilometres per hour?

A) 60 km/h
B) 80 km/h
C) 100 km/h
D) 120 km/h

Answer: B) 80 km/h

Explanation: The car's speed is 80 kilometres per hour. This is calculated by dividing the total distance travelled (240 kilometres) by the total time taken (3 hours). Therefore, 240 km / 3 hours = 80 km/h. This means that the car is travelling at a speed of 80 kilometres per hour.

Question 10: If a train travels 300 kilometres in 4 hours, what is its speed in meters per second?

A) 10 m/s
B) 15 m/s
C) 20.83 m/s
D) 25 m/s

Answer: C) 20.83 m/s

Explanation: To find how fast the train is in meters per second, first change the distance from kilometers to meters. Since 1 kilometre is 1000 meters, 300 kilometres is 300,000 meters. Then, calculate the speed by dividing the distance by the time.

The train travelled 300,000 meters in 4 hours, which is 14,400 seconds. So, speed = 300,000 meters ÷ 14,400 seconds ≈ 20.83 meters per second. The train's speed is about 20.83 meters per second.

Conclusion

Understanding the concepts of races and games is important for mastering aptitude questions. By solving sample questions, calculating time, speed, and distance, and accessing more aptitude questions, you can enhance your skills in this area.

Keep practicing and challenging yourself with various race and game problems to sharpen your aptitude skills. Understanding the concepts thoroughly will not only help you in aptitude tests but also in real-life scenarios where time, speed, and distance calculations are essential.

Time For A Short Quiz

Frequently Asked Questions (FAQs)

1. What are some common race terminologies used in aptitude tests?

In aptitude tests, common race terminologies include speed, distance, time, relative speed, and average speed. Understanding these terms is crucial for solving problems related to races and games efficiently.

2. Why is it important to understand race problems in aptitude tests?

Understanding race problems in aptitude tests helps develop problem-solving skills, enhances logical reasoning abilities, and improves time management during exams. Proficiency in this area can significantly boost overall performance.

3. How can one solve sample questions related to races and games effectively?

To solve sample questions on races and games effectively, practice regularly, understand the basic concepts thoroughly, utilize shortcuts where applicable and focus on improving calculation speed. Seek guidance from experienced mentors or online resources for better clarity.

4. What is the significance of calculating time, speed, and distance in race problems?

Calculating time, speed, and distance accurately is essential in solving race problems as it aids in determining the relative speeds of participants, predicting outcomes of races or games, and making informed decisions based on different scenarios presented in the questions.

5. Where can one access aptitude questions specifically focused on races and games?

Aptitude questions centred on races and games can be accessed through various online platforms offering practice tests, mock exams, or dedicated sections focusing on quantitative aptitude.

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