Races and Games – Aptitude Questions and Answers

Last Updated : 06 Nov, 2024

Race and Games is a very important concept for quantitative aptitude in various competitive exams. In this article, we will explore some of the fundamental concepts of races and games and provide examples of frequently asked questions in these exams.

Prerequisite: Races and Games – Fundamentals

Aptitude Questions on Races and Games

Q 1. In a 100 m race, A beats B by 28 meters. Also, at the finish line, A was 7 seconds ahead of B. Find the time taken by A to complete the race.

Solution:

According to the question, B covers 28 m in 7 seconds. => B’s speed = 28 / 7 = 4 m/s => Time required by B to complete 100 m = 100 / 4 = 25 s Now, A needs 7 s less than B to complete the race. => Time required by A = 25 – 7 = 18 s

Q 2. In a 100 m race, A can give a start of 4 m to B and 6.4 m to C. How many starts can B give to C?

Solution:

If A covers 100 m, B covers 96 m and C covers 93.6 m => When B covers 96 m, C covers 93.6 m => When B covers 100 m, C covers (93.6 / 96) x 100 = 97.5 m Therefore, B can give a start of 100 – 97.5 = 2.5 m to C.

Q 3. A 100-meter race has been completed by two athletes, A and B. If A finishes the race in 10 seconds and B finishes the race in 12 seconds, what is the ratio of their speeds?

Solution:

We can find the ratio of the speeds of A and B using the formula: Ratio of speeds = distance/time. Since both A and B have run the same distance, the ratio of their speeds will be proportional to the inverse of their times. Therefore, we can write the ratio of speeds = B’s time / A’s time. Substituting the given values, we get the ratio of speeds = 12 / 10. Simplifying, we get the ratio of speeds = 6 / 5.

Q 4. In a 5000-meter race, if runner A runs at a speed of 12 meters per second and runner B runs at a speed of 15 meters per second, how many seconds will it take for runner B to finish the race if runner A finishes the race in 20 minutes?

Solution:

We know that runner A finishes the race in 20 minutes, which is equivalent to 20 x 60 = 1200 seconds. We can use the formula: Distance = speed x time. The distance covered by runner A in 1200 seconds is Distance = 12 x 1200 = 14400 meters. We want to find out how many seconds it will take for runner B to finish the race. Let’s assume that it takes runner B t seconds to finish the race. Then, the distance covered by runner B in t seconds is Distance = 15t. Since both runners cover the same distance, we can set up an equation: 14400 = 15t. Solving for t, we get t = 960. Therefore, runner B will finish the race in 960 seconds or 16 minutes

Practice Questions on Races and Games

1. In a 100m race, A beats B by 10m and C by 15m. In the same race, by how many meters does B beat C?

2. A can run a certain distance in 6 minutes. B can cover the same distance in 7.5 minutes. If A gives B a start of 200m, who will win the race?

3. In a game of chess, if A can give B 5 games out of 25 and C 7 games out of 30, how many games can B give C out of 100?

4. A, B, and C run a race. If A gives B a start of 20m and B gives C a start of 30m, then A gives C a start of 44m. The length of the race is 100m. What are the speeds of A, B, and C?

5. In a 200m race, A beats B by 20m and C by 40m. How much does B beat C by?

6. A, B, and C can do a piece of work in 20, 30, and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

7. A can swim 3 times as fast in still water as B. In a river running at 1.5 km/hr, A swims for 52 minutes with the current and returns in 1 hour 8 minutes. How long will B take to swim 3 km in still water?

8. A’s speed is 20% more than B’s. B’s speed is 20% less than C’s. If A covers 33 km in 2 hours, what is C’s speed?

9. In a 100m race, A can give B 10m and C 28m start. If B and C were to run a 100m race, how many meters start can B give to C?

10. A, B, C, and D run a race. A runs twice as fast as B, B runs 1.5 times as fast as C, and C runs twice as fast as D. If D’s speed is 5 km/hr, what is A’s speed?