Take sectional tests or a full 40-question mock on time-speed-distance, trains, boats and streams, circular motion, time and work, and pipes and cisterns with timers and answer review.
This route gives you four sectional sessions and a full mixed mock. Each question runs on a 60-second timer to train both concept clarity and pace.
Time and work, efficiency, and worker-days
Pipes, cisterns, leak, and net rate
Time-speed-distance, trains, and crossing logic
Boats, streams, and circular motion
1. Arjun can complete a wall in 20 days and Diya in 30 days. How long will they take together?
Explanation: Combined rate = 1/20 + 1/30 = 5/60 = 1/12. So together they take 12 days.
2. Rohan is 3 times as efficient as Rahul. Together they finish a job in 9 days. How many days does Rohan alone take?
Explanation: Let Rahul's rate be r. Then Rohan's rate is 3r, so together they work at 4r. Total work = 4r x 9 = 36r. Rohan alone takes 36r / 3r = 12 days.
3. A can do a work in 15 days and B in 20 days. They work together for 6 days, then A leaves. How many more days does B need?
Explanation: LCM of 15 and 20 is 60 units. A does 4 units/day, B does 3 units/day. In 6 days together, they do 42 units. Remaining work = 18 units. B alone takes 18/3 = 6 days.
4. If 12 workers build a house in 20 days, how many workers are needed to build it in 15 days?
Explanation: Total work = 12 x 20 = 240 worker-days. Required workers = 240/15 = 16.
5. Priya can type 1200 words in 30 minutes. How many words can she type in 2.5 hours?
Explanation: Rate = 1200/30 = 40 words per minute. In 2.5 hours = 150 minutes, she types 40 x 150 = 6000 words.
6. A, B and C can complete a task in 12, 15 and 20 days respectively. A and B work for 4 days, then C joins them. In how many more days is the task done?
Explanation: LCM is 60 units. A = 5/day, B = 4/day, C = 3/day. A and B do 9 x 4 = 36 units in 4 days. Remaining = 24 units. A, B and C together do 12 units/day, so they need 2 more days.
7. 15 workers can build a road in 24 days. How many workers are needed to build the same road in 18 days?
Explanation: Total work = 15 x 24 = 360 worker-days. Required workers = 360/18 = 20.
8. Priya is twice as efficient as Rohan. Together they complete a project in 18 days. How long would Priya alone take?
Explanation: Let Rohan's rate be r, then Priya's rate is 2r. Together = 3r. Total work = 3r x 18 = 54r. Priya alone takes 54r/2r = 27 days.
9. 20 men can dig a trench in 18 days. After 6 days, 8 men leave. How many more days are needed?
Explanation: Total work = 20 x 18 = 360 man-days. Work done in 6 days = 120 man-days. Remaining = 240 man-days. Remaining men = 12. Days needed = 240/12 = 20 days.
10. Kiran can do 2/3 of a task in 16 days. In how many days will she complete the full task?
Explanation: If 2/3 of the task takes 16 days, then the full task takes 16 x 3/2 = 24 days.
11. Pipe A fills a tank in 10 hours and Pipe B fills it in 15 hours. If both are opened together, how long will the tank take to fill?
Explanation: Combined rate = 1/10 + 1/15 = 5/30 = 1/6. So the tank fills in 6 hours.
12. A pipe fills a tank in 6 hours, but due to a leak it takes 8 hours. In how many hours can the leak empty the full tank?
Explanation: Leak rate = 1/6 - 1/8 = 1/24 of the tank per hour. So the leak alone empties the tank in 24 hours.
13. An inlet fills a tank in 8 hours and an outlet empties it in 12 hours. If both are opened together when the tank is empty, how long will it take to fill?
Explanation: Net rate = 1/8 - 1/12 = 1/24. So the tank fills in 24 hours.
14. Two pipes fill a tank in 20 and 30 hours respectively. A waste pipe empties it in 40 hours. If all three are opened together, time taken to fill the tank is:
Explanation: Net rate = 1/20 + 1/30 - 1/40 = 7/120. Time = 120/7 = 17.14 hours, about 17.1 hours.
15. Pipe A fills a tank in 9 hours. Pipe B fills it in 12 hours. Pipe A is opened at 6 AM and Pipe B at 9 AM. At approximately what time will the tank be full?
Explanation: By 9 AM, Pipe A fills 3/9 = 1/3 of the tank. Remaining tank = 2/3. Combined rate = 1/9 + 1/12 = 7/36. Time for remaining = (2/3)/(7/36) = 24/7 hours = about 3 hours 26 minutes. So the tank is full at about 12:26 PM.
16. A cistern is 3/5 full. Three pipes fill it in 10, 12 and 15 hours respectively. In how much time will it become full?
Explanation: Combined rate = 1/10 + 1/12 + 1/15 = 1/4 tank per hour. Remaining part = 2/5. Time = (2/5)/(1/4) = 8/5 hours = 1 hour 36 minutes.
17. A leak at the bottom empties a full tank in 8 hours. An inlet fills it in 6 hours. If the tank is full and both start together, what happens?
Explanation: Inlet rate = 1/6, leak rate = 1/8. Net rate = 1/24 filling, not emptying. So the tank never empties while both operate.
18. Pipe A fills 1/3 of a tank in 5 hours. In how many hours will Pipe A fill the whole tank?
Explanation: If 1/3 tank is filled in 5 hours, the full tank is filled in 5 x 3 = 15 hours.
19. Pipe A fills 1/3 of a tank in 5 hours and Pipe B fills 2/5 of the same tank in 8 hours. Working together, they fill the tank in:
Explanation: Pipe A fills full tank in 15 hours, Pipe B fills full tank in 20 hours. Combined rate = 1/15 + 1/20 = 7/60. Time = 60/7 = 8 4/7 hours.
20. A pipe can fill a tank in 4 hours. If the tank is already half full, how much more time will it take?
Explanation: If the whole tank takes 4 hours, half the tank takes 2 hours.
21. Arjun cycles from Delhi to Faridabad, 40 km away, at 20 km/hr and returns at 15 km/hr. His average speed for the round trip is:
Explanation: For equal distances, average speed = 2ab/(a+b) = 2 x 20 x 15 / 35 = 120/7 = 17.14 km/hr.
22. Convert 90 km/hr into m/s.
Explanation: 90 x 5/18 = 25 m/s.
23. A train 200 m long crosses a 300 m bridge in 25 seconds. Its speed is:
Explanation: Total distance = 200 + 300 = 500 m. Speed = 500/25 = 20 m/s = 72 km/hr.
24. Two buses start from opposite ends of a 420 km road at 70 km/hr and 60 km/hr. They meet after:
Explanation: Relative speed = 70 + 60 = 130 km/hr. Time = 420/130 = 42/13 hours, which is about 3 hours 14 minutes.
25. Diya drives at 90 km/hr and catches Arjun driving at 60 km/hr after 4 hours. What was Arjun's head start?
Explanation: Relative speed = 90 - 60 = 30 km/hr. Head start = 30 x 4 = 120 km.
26. A train covers the first 180 km at 90 km/hr and the next 120 km at 60 km/hr. The average speed for the whole journey is:
Explanation: Total distance = 300 km. Time = 180/90 + 120/60 = 2 + 2 = 4 hours. Average speed = 300/4 = 75 km/hr.
27. A train running at 90 km/hr takes 9 seconds to pass a signal post. The length of the train is:
Explanation: 90 km/hr = 25 m/s. Length = 25 x 9 = 225 m.
28. A train passes a standing man in 12 seconds and a 240 m bridge in 36 seconds. The length of the train is:
Explanation: Let train length be L and speed be v. Then L/v = 12 and (L + 240)/v = 36. So 12v + 240 = 36v, hence 240 = 24v and v = 10. Therefore L = 12 x 10 = 120 m.
29. If the speed ratio of two cars is 3:4 and they travel the same distance, the time ratio is:
Explanation: For the same distance, time is inversely proportional to speed. So the ratio is 4:3.
30. Arjun and Diya run around a 600 m track at 10 m/s and 6 m/s in the same direction. They first meet after:
Explanation: Relative speed = 10 - 6 = 4 m/s. Time to gain one full lap = 600/4 = 150 seconds.
31. A boat's speed in still water is 12 km/hr and the current speed is 3 km/hr. Its downstream speed is:
Explanation: Downstream speed = still water speed + stream speed = 12 + 3 = 15 km/hr.
32. A boat covers 32 km upstream in 4 hours and 40 km downstream in 4 hours. The speed of the stream is:
Explanation: Upstream speed = 32/4 = 8 km/hr and downstream speed = 40/4 = 10 km/hr. Stream speed = (10 - 8)/2 = 1 km/hr.
33. A boat can travel 20 km in 2 hours downstream and the same distance in 5 hours upstream. Its speed in still water is:
Explanation: Downstream speed = 10 km/hr and upstream speed = 4 km/hr. Still water speed = (10 + 4)/2 = 7 km/hr.
34. A boat goes 75 km downstream in the same time it goes 45 km upstream. If the speed of the current is 3 km/hr, the speed in still water is:
Explanation: Let still water speed be u. Then 75/(u+3) = 45/(u-3). Solving gives u = 12 km/hr.
35. Two friends run on a 400 m track in opposite directions at 5 m/s and 3 m/s. Their first meeting at the starting point happens after:
Explanation: Lap times are 400/5 = 80 sec and 400/3 sec. Their first common return to start is after the LCM, which is 400 seconds.
36. Two runners move on a 1000 m circular track in opposite directions at 8 m/s and 12 m/s. They first meet after:
Explanation: Relative speed = 8 + 12 = 20 m/s. Time = 1000/20 = 50 sec.
37. Meera rows downstream for 2 hours and covers 18 km. She takes 4.5 hours to return. The speed of the current is:
Explanation: Downstream speed = 18/2 = 9 km/hr and upstream speed = 18/4.5 = 4 km/hr. Stream speed = (9 - 4)/2 = 2.5 km/hr.
38. Arjun and Diya run on a 500 m circular track at 8 m/s and 2 m/s in the same direction. In how many seconds does Arjun lap Diya for the 5th time?
Explanation: Relative speed = 8 - 2 = 6 m/s. One lap gain takes 500/6 = 83.33 sec. For the 5th lap gain, time = 5 x 83.33 = 416.7 sec.
39. The speed of a boat in still water is 10 km/hr. It goes 91 km downstream and returns in 20 hours. The speed of the stream is:
Explanation: Let stream speed be v. Then 91/(10+v) + 91/(10-v) = 20. Solving gives v = 3 km/hr.
40. Three athletes run a 1200 m circular track in 80, 100, and 120 seconds. They first all meet at the starting point after:
Explanation: The time when all return to start together is LCM(80, 100, 120) = 600 seconds.
41. A can finish a job in 18 days. B is 50% more efficient than A. Working together, they finish the job in:
Explanation: If A's rate is 1 unit, B's rate is 1.5 units. A alone takes 18 days, so total work = 18 rate-units. Together rate = 2.5 units/day. Time $=18/2.5=7.2$ days.
42. Two inlet pipes fill a tank in 12 hours and 18 hours. An outlet empties it in 24 hours. If all are opened together, the tank fills in:
Explanation: Net rate $=1/12+1/18-1/24$. Using LCM 72, rate $=(6+4-3)/72=7/72$ tank/hour. Time $=72/7=10.29$ hours.
43. A 180 m train crosses a platform in 18 seconds at 72 km/hr. What is the platform length?
Explanation: 72 km/hr = 20 m/s. Total distance covered in 18 seconds = $20\times18=360$ m. Platform length = 360 - 180 = 180 m.
44. A car covers one-third of a journey at 40 km/hr and the remaining two-thirds at 80 km/hr. The average speed is:
Explanation: Let total distance be 3D. Time = $D/40 + 2D/80 = D/40 + D/40 = D/20$. Average speed $=3D/(D/20)=60$ km/hr.
45. A boat covers 48 km downstream in 3 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?
Explanation: Downstream speed = 48/3 = 16 km/hr. Upstream speed = 48/6 = 8 km/hr. Still water speed $=(16+8)/2=12$ km/hr.