Races and Games for Competitive Exam Preparation

Races and Games

Q. A and B can complete a task in 10 days and 15 days respectively. If they work together for 5 days, how much of the task is left?

A. 1/3
B. 1/4
C. 1/5
D. 1/6

Solution

A's rate = 1/10, B's rate = 1/15. Combined rate = 1/10 + 1/15 = 1/6. Work done in 5 days = 5/6. Remaining = 1 - 5/6 = 1/6.

Correct Answer: A — 1/3

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Q. A and B can complete a work in 12 days and 15 days respectively. If they work together, how many days will they take to complete the work?

A. 6 days
B. 7 days
C. 8 days
D. 9 days

Solution

A's work rate = 1/12, B's work rate = 1/15. Combined work rate = 1/12 + 1/15 = 5/60 = 1/12. Time taken = 12 days.

Correct Answer: C — 8 days

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Q. A and B can complete a work in 12 days and 15 days respectively. If they work together, how long will it take them to complete the work?

A. 6 days
B. 8 days
C. 10 days
D. 5 days

Solution

A's work rate = 1/12, B's work rate = 1/15. Combined rate = 1/12 + 1/15 = 5/60 = 1/12. Time taken = 12 days.

Correct Answer: B — 8 days

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Q. A can complete a race in 120 seconds, while B can complete it in 180 seconds. How much time will A be ahead of B when they finish the race?

A. 30 seconds
B. 40 seconds
C. 50 seconds
D. 60 seconds

Solution

A finishes in 120 seconds, B in 180 seconds. A is ahead by 180 - 120 = 60 seconds.

Correct Answer: B — 40 seconds

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Q. A can finish a race in 100 seconds, while B can finish it in 120 seconds. If they start together, how much time will A be ahead of B when they finish the race?

A. 20 seconds
B. 15 seconds
C. 10 seconds
D. 5 seconds

Solution

A's speed = 1/100, B's speed = 1/120. Time taken by A to finish = 100 seconds, B takes 120 seconds. A is ahead by 120 - 100 = 20 seconds.

Correct Answer: A — 20 seconds

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Q. A can finish a race in 100 seconds, while B finishes it in 120 seconds. What percentage faster is A than B?

A. 20%
B. 25%
C. 15%
D. 30%

Solution

Speed of A = 1/100, Speed of B = 1/120. Percentage faster = ((120 - 100) / 120) * 100 = 16.67%.

Correct Answer: B — 25%

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Q. A can run 10 km in 50 minutes. What is his speed in km/h?

A. 12 km/h
B. 10 km/h
C. 8 km/h
D. 15 km/h

Solution

Speed = Distance / Time = 10 km / (50/60) hours = 12 km/h.

Correct Answer: A — 12 km/h

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Q. A can run 20% faster than B. If B can run 30 km in 3 hours, how far can A run in the same time?

A. 36 km
B. 32 km
C. 30 km
D. 28 km

Solution

B's speed = 30 km / 3 hours = 10 km/h. A's speed = 10 km/h * 1.2 = 12 km/h. Distance A can run in 3 hours = 12 km/h * 3 hours = 36 km.

Correct Answer: B — 32 km

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Q. A can run 20% faster than B. If B can run 30 km in 3 hours, how much distance can A cover in the same time?

A. 36 km
B. 32 km
C. 30 km
D. 28 km

Solution

B's speed = 30 km / 3 hours = 10 km/h. A's speed = 10 km/h * 1.2 = 12 km/h. Distance A can cover in 3 hours = 12 km/h * 3 hours = 36 km.

Correct Answer: B — 32 km

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Q. A can run a distance in 30 minutes, while B can run the same distance in 45 minutes. What is the ratio of their speeds?

A. 3:2
B. 2:3
C. 1:1
D. 4:3

Solution

Speed is inversely proportional to time. Ratio of speeds = 45:30 = 3:2.

Correct Answer: A — 3:2

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Q. A can run a race in 100 seconds, while B can run it in 120 seconds. If they start together, how much time will A lead B after 1 minute?

A. 20 seconds
B. 25 seconds
C. 30 seconds
D. 15 seconds

Solution

A's speed = 1/100, B's speed = 1/120. In 60 seconds, A covers 60/100 = 0.6 km, B covers 60/120 = 0.5 km. Lead = 0.6 - 0.5 = 0.1 km. Time lead = 0.1 / (1/100) = 10 seconds.

Correct Answer: B — 25 seconds

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Q. A cyclist covers a distance of 90 km in 3 hours. What is his average speed?

A. 25 km/h
B. 30 km/h
C. 20 km/h
D. 35 km/h

Solution

Average speed = Total distance / Total time = 90 km / 3 hours = 30 km/h.

Correct Answer: B — 30 km/h

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Q. A cyclist travels at a speed of 15 km/h. How long will it take to cover 45 km?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

Time = Distance / Speed = 45 km / 15 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A jogger runs at a speed of 8 km/h. How far can he run in 45 minutes?

A. 5 km
B. 6 km
C. 7 km
D. 4 km

Solution

Distance = Speed * Time = 8 km/h * (45/60) hours = 6 km.

Correct Answer: A — 5 km

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Q. A jogs at a speed of 8 km/h and B jogs at 10 km/h. If they start together, how far apart will they be after 30 minutes?

A. 2 km
B. 1 km
C. 1.5 km
D. 3 km

Solution

Distance covered by A in 0.5 hours = 8 km/h * 0.5 = 4 km. Distance covered by B = 10 km/h * 0.5 = 5 km. Difference = 5 km - 4 km = 1 km.

Correct Answer: A — 2 km

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Q. If A can complete a race in 40 minutes and B can complete it in 50 minutes, what is the ratio of their speeds?

A. 5:4
B. 4:5
C. 2:3
D. 3:2

Solution

Speed is inversely proportional to time. Ratio of speeds = 50:40 = 5:4.

Correct Answer: A — 5:4

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Q. If A can complete a race in 40 seconds and B can complete it in 50 seconds, what is the ratio of their speeds?

A. 5:4
B. 4:5
C. 2:1
D. 1:2

Solution

Speed is inversely proportional to time. Ratio of speeds = 50:40 = 5:4.

Correct Answer: A — 5:4

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Q. If A can complete a task in 8 hours and B can complete it in 12 hours, how long will it take them to complete the task together?

A. 4.8 hours
B. 5 hours
C. 5.5 hours
D. 6 hours

Solution

A's rate = 1/8, B's rate = 1/12. Together = 1/8 + 1/12 = 5/24. Time = 24/5 = 4.8 hours.

Correct Answer: A — 4.8 hours

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Q. If A can finish a race in 45 seconds and B in 60 seconds, what is the percentage difference in their speeds?

A. 25%
B. 33.33%
C. 20%
D. 15%

Solution

Speed ratio = 60:45 = 4:3. Percentage difference = (4-3)/3 * 100 = 33.33%.

Correct Answer: B — 33.33%

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Q. If A can run a distance in 40 minutes and B can run the same distance in 60 minutes, what is the ratio of their speeds?

A. 3:2
B. 2:3
C. 1:1
D. 4:3

Solution

Speed is inversely proportional to time. Ratio of speeds = 60:40 = 3:2.

Correct Answer: A — 3:2

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Q. If a car travels 60 km in 1 hour, how long will it take to travel 150 km at the same speed?

A. 2 hours
B. 2.5 hours
C. 3 hours
D. 3.5 hours

Solution

Speed = 60 km/h. Time = Distance / Speed = 150 km / 60 km/h = 2.5 hours.

Correct Answer: C — 3 hours

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Q. If a car travels at a speed of 60 km/h, how long will it take to cover a distance of 150 km?

A. 2 hours
B. 2.5 hours
C. 3 hours
D. 3.5 hours

Solution

Time = Distance / Speed = 150 km / 60 km/h = 2.5 hours.

Correct Answer: B — 2.5 hours

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Q. If A is twice as fast as B and B can cover 30 km in 2 hours, how far can A cover in 1 hour?

A. 30 km
B. 20 km
C. 15 km
D. 25 km

Solution

B's speed = 30 km / 2 hours = 15 km/h. A's speed = 2 * 15 km/h = 30 km/h. Distance A can cover in 1 hour = 30 km.

Correct Answer: A — 30 km

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Q. If a runner completes a 400 m track in 50 seconds, what is his speed in km/h?

A. 7.2 km/h
B. 8 km/h
C. 9 km/h
D. 10 km/h

Solution

Speed = Distance / Time = 400 m / 50 s = 8 m/s = 8 * 18/5 = 28.8 km/h.

Correct Answer: A — 7.2 km/h

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Q. If a runner completes a 400 m track in 50 seconds, what is his speed in m/s?

A. 6 m/s
B. 8 m/s
C. 7 m/s
D. 5 m/s

Solution

Speed = Distance / Time = 400 m / 50 s = 8 m/s.

Correct Answer: A — 6 m/s

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Races and Games

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