Time, Speed & Work: Practice Questions with Answers
Speed and distance, trains, boats, time and work, and pipes. Try each question first: tap an option to check it, and the explanation appears below.
Question 1Easy
A train 180 m long crosses a pole in 18 seconds. What is the speed of the train in km/h?
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✅ B. 36 km/h
To pass a pole, the train covers only its own length. Speed = 180 m ÷ 18 s = 10 m/s. To change m/s into km/h, multiply by 18/5: 10 × 18/5 = 36 km/h.
Question page →Question 2Medium
A cyclist goes from one town to another at 40 km/h and comes back by the same road at 60 km/h. What is the average speed for the whole journey?
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✅ B. 48 km/h
Average speed = total distance ÷ total time, not the average of the two speeds. For equal distances, average speed = 2ab ÷ (a + b) = 2 × 40 × 60 ÷ (40 + 60) = 48 km/h. The simple average (50 km/h) is wrong because more time is spent at the slower speed.
Question page →Question 3Medium
A cyclist goes from one town to another at 30 km/h and comes back by the same road at 60 km/h. What is the average speed for the whole journey?
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✅ D. 40 km/h
Average speed = total distance ÷ total time, not the average of the two speeds. For equal distances, average speed = 2ab ÷ (a + b) = 2 × 30 × 60 ÷ (30 + 60) = 40 km/h. The simple average (45 km/h) is wrong because more time is spent at the slower speed.
Question page →Question 4Easy
A train 420 m long crosses a pole in 12 seconds. What is the speed of the train in km/h?
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✅ B. 126 km/h
To pass a pole, the train covers only its own length. Speed = 420 m ÷ 12 s = 35 m/s. To change m/s into km/h, multiply by 18/5: 35 × 18/5 = 126 km/h.
Question page →Question 5Hard
A can do a job in 12 days and B in 24 days. They work together for 2 days, and then A leaves. In how many more days will B finish the job?
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✅ C. 18 days
Together they do 1/12 + 1/24 = 1/8 of the job per day, so in 2 days they finish 1/4 of it. The part left is 3/4 of the job. B alone does 1/24 of the job per day, so B needs 3/4 × 24 = 18 more days.
Question page →Question 6Hard
A is three times as efficient as B. Working together, they finish a job in 24 days. How many days would A take to finish the job alone?
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✅ D. 32 days
If B does 1 unit of work per day, A does 3 units, so together they do 4 units per day. The whole job is 4 × 24 = 96 units. A alone takes 96 ÷ 3 = 32 days, and B alone would take 96 days. A, being faster, needs fewer days than B but more than the 24 days they take together.
Question page →Question 7Medium
A boat moves at 7 km/h in still water and the stream flows at 3 km/h. How long will the boat take to go 40 km downstream and come back?
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✅ B. 14 hours
Downstream the stream helps: 7 + 3 = 10 km/h, so going takes 40 ÷ 10 = 4 hours. Upstream the stream works against it: 7 − 3 = 4 km/h, so coming back takes 40 ÷ 4 = 10 hours. Total time = 14 hours.
Question page →Question 8Medium
A train 580 m long is running at 216 km/h. How long will it take to cross a platform 1700 m long?
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✅ C. 38 seconds
To cross a platform, the train covers its own length plus the platform: 580 + 1700 = 2280 m. Speed = 216 × 5/18 = 60 m/s. Time = 2280 ÷ 60 = 38 seconds. Using only the train's length gives 9.67 seconds, which is the time to pass a pole, not a platform.
Question page →Question 9Medium
A train 200 m long is running at 72 km/h. How long will it take to cross a platform 120 m long?
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✅ D. 16 seconds
To cross a platform, the train covers its own length plus the platform: 200 + 120 = 320 m. Speed = 72 × 5/18 = 20 m/s. Time = 320 ÷ 20 = 16 seconds. Using only the train's length gives 10 seconds, which is the time to pass a pole, not a platform.
Question page →Question 10Medium
Pipe A can fill a tank in 12 hours and pipe B can empty the full tank in 18 hours. If both pipes are opened together on an empty tank, how long will it take to fill?
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✅ B. 36 hours
In one hour A fills 1/12 of the tank and B empties 1/18. The net filling per hour is 1/12 − 1/18 = 1/36. So the tank fills in 36 hours. Shortcut: ab ÷ (b − a) = 216 ÷ 6 = 36. Adding the rates would treat B as a filling pipe, which is wrong.
Question page →Question 11Easy
A train 300 m long crosses a pole in 10 seconds. What is the speed of the train in km/h?
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✅ D. 108 km/h
To pass a pole, the train covers only its own length. Speed = 300 m ÷ 10 s = 30 m/s. To change m/s into km/h, multiply by 18/5: 30 × 18/5 = 108 km/h.
Question page →Question 12Easy
A train 600 m long crosses a pole in 15 seconds. What is the speed of the train in km/h?
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✅ B. 144 km/h
To pass a pole, the train covers only its own length. Speed = 600 m ÷ 15 s = 40 m/s. To change m/s into km/h, multiply by 18/5: 40 × 18/5 = 144 km/h.
Question page →Question 13Easy
30 workers can build a wall in 25 days. How many days will 5 workers take to build the same wall, working at the same rate?
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✅ C. 150 days
The total work is 30 × 25 = 750 worker-days. More workers means fewer days, so divide: 750 ÷ 5 = 150 days. Multiplying instead (4.17 days) would mean more workers take longer, which cannot be right.
Question page →Question 14Medium
Pipe A can fill a tank in 4 hours and pipe B can empty the full tank in 6 hours. If both pipes are opened together on an empty tank, how long will it take to fill?
Show answerAnswer
✅ D. 12 hours
In one hour A fills 1/4 of the tank and B empties 1/6. The net filling per hour is 1/4 − 1/6 = 1/12. So the tank fills in 12 hours. Shortcut: ab ÷ (b − a) = 24 ÷ 2 = 12. Adding the rates would treat B as a filling pipe, which is wrong.
Question page →Question 15Hard
Two trains, 310 m and 80 m long, are running on parallel tracks in opposite directions at 36 km/h and 72 km/h. How long will they take to cross each other completely?
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✅ B. 13 seconds
In opposite directions, the speeds add: 36 + 72 = 108 km/h = 108 × 5/18 = 30 m/s. To cross completely, they cover both lengths: 310 + 80 = 390 m. Time = 390 ÷ 30 = 13 seconds. In the same direction the speeds would subtract instead.
Question page →Question 16Medium
A train 340 m long is running at 180 km/h. How long will it take to cross a platform 610 m long?
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✅ A. 19 seconds
To cross a platform, the train covers its own length plus the platform: 340 + 610 = 950 m. Speed = 180 × 5/18 = 50 m/s. Time = 950 ÷ 50 = 19 seconds. Using only the train's length gives 6.8 seconds, which is the time to pass a pole, not a platform.
Question page →Question 17Easy
A can finish a piece of work in 20 days and B can finish it in 30 days. How many days will they take working together?
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✅ C. 12 days
In one day A does 1/20 of the work and B does 1/30. Together they do 1/20 + 1/30 = 1/12 of the work per day. So the whole work takes 12 days. Shortcut: ab ÷ (a + b) = 600 ÷ 50 = 12. Together they must be faster than either one alone.
Question page →Question 18Medium
Pipe A can fill a tank in 12 hours and pipe B can empty the full tank in 20 hours. If both pipes are opened together on an empty tank, how long will it take to fill?
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✅ D. 30 hours
In one hour A fills 1/12 of the tank and B empties 1/20. The net filling per hour is 1/12 − 1/20 = 1/30. So the tank fills in 30 hours. Shortcut: ab ÷ (b − a) = 240 ÷ 8 = 30. Adding the rates would treat B as a filling pipe, which is wrong.
Question page →Question 19Medium
Pipe A can fill a tank in 8 hours and pipe B can empty the full tank in 12 hours. If both pipes are opened together on an empty tank, how long will it take to fill?
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✅ A. 24 hours
In one hour A fills 1/8 of the tank and B empties 1/12. The net filling per hour is 1/8 − 1/12 = 1/24. So the tank fills in 24 hours. Shortcut: ab ÷ (b − a) = 96 ÷ 4 = 24. Adding the rates would treat B as a filling pipe, which is wrong.
Question page →Question 20Medium
A train 1070 m long is running at 216 km/h. How long will it take to cross a platform 490 m long?
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✅ C. 26 seconds
To cross a platform, the train covers its own length plus the platform: 1070 + 490 = 1560 m. Speed = 216 × 5/18 = 60 m/s. Time = 1560 ÷ 60 = 26 seconds. Using only the train's length gives 17.83 seconds, which is the time to pass a pole, not a platform.
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