Races and Games Solved Questions and Answers (original) (raw)

Last Updated : 28 Jul, 2025

Races and Games problems involve calculating and comparing speeds, distances, or time taken by participants in competitive scenarios like running races or sports.

**Races and Games questions and answers are provided below for you to learn and practice.

**Question 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

**Question 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.

**Question 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.

**Question 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.

**Question 5: In a 200 m race, A beats B by 50 meters. Also, at the finish line, A was 10 seconds ahead of B. Find the time taken by A to complete the race.

**Solution:

B covers 50 m in 10 seconds.
Speed of B = 50 m / 10 s = 5 m/s
Time required by B to complete 200 m = 200 m / 5 m/s = 40 s
A is 10 seconds ahead, so A takes 40 - 10 = **30 seconds to complete the race.

**Question 6: In a 150 m race, A can give a start of 10 meters to B and 20 meters to C. How many starts can B give to C?

**Solution:

If A runs 150 m, B covers 140 m, and C covers 130 m.
When B runs 140 m, C covers 130 m.
When B runs 150 m, C covers (130 / 140) × 150 = 139.29 m.
Therefore, B can give a start of 150 m - 139.29 m = **10.71 meters to C.

**Question 7: In a 400-meter race, if A finishes the race in 18 seconds and B finishes the race in 22 seconds, what is the ratio of their speeds?

**Solution:

Speed of A = 400 m / 18 s = 22.22 m/s
Speed of B = 400 m / 22 s = 18.18 m/s
Ratio of their speeds = Speed of A / Speed of B = 22.22 / 18.18 = **11:9

**Question 8: In a game of billiards:

**How many points can B give C in a game of 150?

**Solution:

**Given:

Player A : Player B = 75 : (75 - 15) = 75 : 60
Player A : Player C = 75 : (75 - 25) = 75 : 50

\frac{B}{C} = \left( \frac{B}{A} \times \frac{A}{C} \right) = \left( \frac{60}{75} \times \frac{75}{50} \right) = \frac{60}{50} = \frac{6}{5}

So,
B : C = 6 : 5 = 150 : 125

∴B can give C 25 points in a game of 150.