Races and Games - Solved Questions and Answers

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:

• Player A can give B 15 points in a game of 75.
• Player A can give C 25 points in a game of 75.

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.