time and distance, time & work, basic algebraic identities - Question Bank
1. Two trains, A and B, are running on parallel tracks in opposite directions. Train A travels at 70 km/hr and Train B at 80 km/hr. If the length of Train A is 200 meters and Train B is 250 meters, how long will it take for them to cross each other completely?
2. A person walks a distance of 3 km in 30 minutes. What is his speed in km/hr?
3. If x = 7, y = 2, what is the value of (x-y)^2?
4. If x+y+z = 0, then x^3+y^3+z^3 is equal to:
5. A can complete a work in 40 days. B can do it in 60 days. They work together for 10 days. The remaining work is done by C alone in 15 days. In how many days can C alone complete the work?
6. A, B, and C can complete a work in 10 days. If A alone can do it in 20 days and B alone can do it in 30 days, in how many days can C alone do it?
7. A boat moves upstream at 8 km/hr and downstream at 12 km/hr. What is the speed of the boat in still water?
8. Two trains travelling in the same direction at 40 km/hr and 35 km/hr cross each other in 4 minutes. What is the length of the longer train?
9. A train travelling at 60 km/hr passes a man standing on the platform in 15 seconds. What is the length of the train?
10. What is the value of (a+b+c)^2 - (a+b-c)^2?
11. If x - 1/x = 4, what is the value of x^2 + 1/x^2?
12. A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days can they together finish the work?
13. A and B can complete a work in 8 days. B and C can complete it in 12 days. A and C can complete it in 15 days. In how many days can A alone complete the work?
14. Two men can do a piece of work in 6 days. If one of them can do it alone in 10 days, in how many days can the second man do it alone?
15. A train takes 20 seconds to cross a pole and 30 seconds to cross a platform 100 meters long. What is the speed of the train?
16. A man travels from city A to city B at 40 km/hr and returns from city B to city A at 60 km/hr. What is the average speed for the entire journey?
17. If x + 1/x = 5, what is the value of x^2 + 1/x^2?
18. What is the value of (a+b)^2 + (a-b)^2?
19. If the sum of the cubes of two consecutive integers is 91, what are the integers?
20. A, B, and C can complete a work in 10, 12, and 15 days respectively. They start working together. After 2 days, B leaves. In how many days will A and C complete the remaining work?
21. P and Q can complete a work in 12 days and 18 days respectively. They start working together. After 6 days, P leaves. In how many days will Q complete the remaining work?
22. A can do a work in 15 days. B can do the same work in 20 days. They work together for 4 days. The remaining work is completed by A alone. In how many days will A complete the remaining work?
23. A train travelling at 72 km/hr crosses a bridge in 30 seconds. What is the length of the bridge if the length of the train is 150 meters?
24. A boat takes 6 hours to travel downstream from point A to point B. It takes 10 hours to travel upstream from B to A. If the speed of the stream is 2 km/hr, what is the distance between A and B?
25. A person walks 4 km/hr. How much distance will he cover in 2 hours and 30 minutes?
26. Two trains start from the same station at the same time in opposite directions. One travels at 50 km/hr and the other at 60 km/hr. How far apart will they be after 3 hours?
27. A car travels 120 km in 3 hours. If it increases its speed by 10 km/hr, how much time will it take to cover the same distance?
28. If x = 3, what is the value of (2x+3)^2?
29. What is the value of (a+b)(a-b)?
30. If x^2 - y^2 = 80 and x - y = 8, what is the value of x + y?
31. A and B can complete a work in 10 days and 15 days respectively. They work together for 5 days, and then A leaves. In how many days will B complete the remaining work?
32. If A can do a job in 30 days and B can do it in 45 days, and they work together for 10 days, how much of the job is left?
33. A man can row a boat at a speed of 10 km/hr in still water. If the speed of the stream is 2 km/hr, what is the time taken by him to cover a distance of 48 km downstream?
34. Two trains of lengths 100m and 150m are running on parallel tracks in the same direction with speeds 60 km/hr and 40 km/hr respectively. In what time will the faster train cross the slower train?
35. A train moving at 45 km/hr takes 10 seconds to pass a signal. What is the length of the train?
36. If a = 5, b = 3, what is the value of (a+b)^2?
37. What is the value of (a+b)^2 - (a-b)^2?
38. If x + y = 10 and xy = 21, what is the value of x^2 + y^2?
39. The sum of squares of two consecutive even numbers is 244. What are the numbers?
40. P can do a work in 10 days. Q can do the same work in 15 days. They start working together, but P leaves after 5 days. In how many days will Q complete the remaining work?
41. Ram can do a work in 5 days and Shyam can do the same work in 7 days. They work together for 3 days. The remaining work is done by Ram alone. In how many days will Ram complete the remaining work?
42. A, B, and C can complete a work in 12, 15, and 20 days respectively. If they work together, how many days will they take to complete the work?
43. A can complete a work in 20 days and B can complete the same work in 30 days. In how many days can they complete the work together?
44. If a man can do a piece of work in 10 days, what fraction of the work can he do in 1 day?
45. A train crosses a platform 100 meters long in 10 seconds and a pole in 5 seconds. What is the length of the train?
46. A boat travels downstream at 20 km/hr and upstream at 10 km/hr. What is the speed of the boat in still water?
47. A man walks at a speed of 5 km/hr. How much distance will he cover in 1.5 hours?
48. Two cyclists start from the same point at the same time. One cycles north at 10 km/hr and the other cycles south at 15 km/hr. How far apart will they be after 2 hours?
49. A car travels at a speed of 60 km/hr. How long will it take to cover a distance of 180 km?
50. A train travels a distance of 300 km in 4 hours. What is its speed in km/hr?