Time, Speed and Distance Multiple Choice Questions | Problem on Trains & Boat and Streams
1. A boat goes 15 km upstream in 80 minutes. The speed of the stream is 5 km/h. The speed of the boat in still water is?
Solution:-15 km upstream in 80 minutes Æ 15/1.33 = 11.25 kmph. (upstream speed of the boat). Thus, still water speed of the boat = 11.25 + 5 = 16.25 kmph
2. The speed of the boat in still water is 12 km/h and the speed of the stream is 2 km/h. A distance of 8 km, going upstream, is covered in?
Solution:-8/(12 – 2) = 8/10 = 0.8 hours
3. Two trains are running on parallel lines in the same direction at speeds of 40 kmph and 20 kmph respectively. The faster train crosses a man in the second train in 36 seconds. The length of the faster train is
Solution:- (20 x 5/18) x 36 = Lt -> Lt= 200 m
4. A boat goes 40 km upstream in 8 h and a distance of 49 km downstream in 7 h. The speed of the boat in still water is?
Solution:-Upstream speed = 40/8 = 5 kmph. Downstream speed = 49/7 = 7 kmph. Speed in still water = average of upstream and downstream speed = 6 kmph.
5. A man rows 6 km/h in still water. If the river is running at 3 km per hour, it takes him 45 minutes to row to a place and back. How far is the place?
Solution:-x/9 + x/3 = 3/4 -> 4x/9 = 3/4 -> x = 27/16 kms = 1.6875 kms
6. A boat sails down the river for 10 km and then up the river for 6 km. The speed of the river flow is 1 km/h. What should be the minimum speed of the boat for the trip to take a maximum of 4 hours?
Solution:-Solve through options. For option (c) at 4 kmph, the boat would take exactly 4 hours to cover the distance
7 . A boat sails downstream from point A to point B, which is 10 km away from A, and then returns to A. If the actual speed of the boat (in still water) is 3 km/h, the trip from A to B takes 8 hours less than that from B to A. What must the actual speed of the boat for the trip from A to B to take exactly 100 minutes?
Solution:-?
8. A train requires 7 seconds to pass a pole while it requires 25 seconds to cross a stationary train which is 378 meters long. Find the speed of the train.
Solution:-7 x St = Lt 25 x St = Lt+ 378 Solving, St = 21 m/sec. = 21 x 18/5 = 75.6 kmph.
9. A motorboat went downstream for 28 km and immediately returned. It took the boat twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.
Solution:-From the situation described in the first condition itself, we can see that the speed of coming back has to be double the speed of going downstream. Checking the options, only option (a) fits this condition i.e. Downstream speed = 2 x Upstream speed.
10. Sonu and Monu run a race of 2000 m. First, Sonu gives Monu a start of 200 m and beats him by 30 s. Next, Sonu gives Monu a start of 3 min and is beaten by 1000 meters. Find the time in minutes in which Sonu and Monu can run the race separately.
Solution:-?
11.The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speed is 70 km/h.
Solution:-The ratio of time for the travel is 4:3 (Sinhagad to Deccan Queen). Hence, the ratio of speeds would be 3:4. Since the sum of their average speeds is 70 kmph, their respective speeds would be 30 and 40 kmph respectively. Use allegation to get the answer as 34.28 kmph.
12. Walking at 3/4 of his normal speed, Abhishek is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and his office is
Solution:- When the speed goes down to three fourth (i.e. 75%) time will go up to 4/3rd (or 133.33%) of the original time. Since the extra time required is 16 minutes, it should be equated to 1/3rd of the normal time. Hence, the usual time required will be 48 minutes.
13. Divya and Manisha travel the same distance at the rate of 6 km per hour and 10 km per hour respectively. If Divya takes 30 minutes longer than Manish, the distance traveled by each is
Solution:-. Since the ratio of speeds is 3:5, the ratio of times would be 5:3. The difference in the times would be 2 (if looked at in the 5:3 ratio context.) Further, since Divya takes 30 minutes longer, 2 corresponds to 30. Hence, using the unitary method, 5 will correspond to 75 and 3 will correspond to 45 minutes. Hence at 10 kmph, Manisha would travel 7.5 km.
14. Two trains for Mumbai leave Delhi at 6: 00 a.m. and 6: 45 a.m. and travel at 100 kmph and 136 kmph respectively. How many kilometers from Delhi will the two trains be together?
Solution:- The train that leaves at 6 am would be 75 km ahead of the other train when it starts. Also, the relative speed being 36 kmph, the distance from Mumbai would be: (75/36) x 136 = 283.33 km
15. Two trains, Calcutta Mail and Bombay Mail start at the same time from stations Kolkata and Mumbai respectively towards each other. After passing each other, they take 12 hours and 3 hours to reach Mumbai and Kolkata respectively. If the Calcutta Mail is moving at the speed of 48 km/h, the speed of the Bombay Mail is?
Solution:-?
16. Shyam’s house, his office, and his gym are all equidistant from each other. The distance between any 2 of them is 4 km. Shyam starts walking from his gym in a direction parallel to the road connecting his office and his house and stops when he reaches a point directly east of his office. He then reverses direction and walks till he reaches a point directly south of his office. The total distance walked by Shyam is?
Solution:-?
17. Lonavala and Khandala are two stations 600 km apart. A train starts from Lonavala and moves towards Khandala at the rate of 25 km/h. After two hours, another train starts from Khandala at the rate of 35 km/h. How far from Lonavala will they will cross each other?
Solution:- When the train from Khandala starts off, the train from Lonavala will already have covered 50 km. Hence, 550 km at a relative speed of 60 kmph will take 550/60 hrs. From this, you can get the answer as: 50 + (550/60) * 25 = 279.166 km.
18. Walking at 3/4 of his normal speed, a man takes 2(1/2) hours more than the normal time. Find the normal time.
Solution:- When his speed becomes 3/4th, his time would increase by 1/3rd. Thus, the normal time = 7.5 hrs. (since increased time = 2.5 hrs).
19. Sonu walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long would it have taken for him to walk both ways?
Solution:-. Since he gains 2 hours by driving both ways (instead of walking one way) the time taken for driving would be 2 hours less than the time taken for walking. Hence, he stands to lose another two hours by walking both ways. Hence his total time should be 8 hrs 45 minutes
20. Sambhu beats Kalu by 30 meters or 10 seconds. How much time was taken by Sambhu to complete a race 1200 meters.
Solution:- . Kalu’s speed = 3 m/s. For 1200 m, Kalu would take 400 seconds and Sambhu would take 10 seconds less. Hence, 390 seconds.
21. A train moves at a constant speed of 120 km/h for one kilometer and at 40 kmph for the next one kilometer. What is the average speed of the train?
Solution:-?
22. A plane left half an hour later than the scheduled time and in order to reach its destination 1500 kilometres away in time, it had to increase its speed by 33.33 percent over its usual speed. Find its increased speed?
Solution:- .. By increasing the speed by 33.33%, it would be able to reduce the time taken for travel by 25%. But since this is just able to overcome a time delay of 30 minutes, 30 minutes must be equivalent to 25% of the time originally taken. Hence, the original time must have been 2 hours and the original speed would be 750 kmph. Hence, the new speed would be 1000 kmph.
23. If Arun had walked 1 km/h faster, he would have taken 10 minutes less to walk 2 kilometres. What is Arun’s speed of walking?
Solution:- Solve through options using trial and error. For usual speed 3 kmph we have: Normal time -> 2/3 hours = 40 minutes. At 4 kmph the time would be 2/4 hrs, this gives us a distance of 10 minutes. Hence option (c) is correct.
24. A passenger train takes 2 h less for a journey of 300 kilometers if its speed is increased by 5 kmph over its usual speed. Find the usual speed.
Solution:- The required speed s would be satisfying the equation: 300/s – 300/(s + 5) = 2 Solving for s from the options it is clear that s = 25
25. A journey of 192 km takes 2 hours less by a fast train than by a slow train. If the average speed of the slow train be 16 kmph less than that of a fast train, what is the average speed of the faster train?
Solution:- Solve this question using the values given in the options. Option (d) can be seen to fit the situation given by the problem as it gives us the following chain of thought: If the average speed of the faster train is 48 kmph, the average speed of the slower train would be 32 kmph. In this case, the time taken by the faster train (192/48 = 4 hours) is 2 hours lesser than the time taken by the slower train (192/32 = 6 hours). This satisfies the condition given in the problem and hence option (d) is correct.
26. Harsh and Vijay move towards Hosur starting from IIM, Bangalore, at a speed of 40 km/h and 60 km/h respectively. If Vijay reaches Hosur 200 minutes earlier then Harsh, what is the distance between IIM, Bangalore, and Hosur?
Solution:-At 40 kmph, Harsh would cover (200/60) ¥ 40 km. = 400/3 km. = 133.33 km. This represents the distance by which Vijay would be ahead of Harsh, when Vijay reaches the endpoint means in essence that Vijay must have traveled for 133.33/20 hours -> 6.66 hours Hence, the distance is 60 x 6.66 = 400 km.
27. A car driver, driving in a fog, passes a pedestrian who was walking at the rate of 2 km/h in the same direction. The pedestrian could see the car for 6 minutes and it was visible to him up to a distance of 0.6 km. What was the speed of the car?
Solution:- In 6 minutes, the car goes ahead by 0.6 km. Hence, the the relative speed of the car with respect to the pedestrian is equal to 6 kmph, since, the pedestrian is walking at 2 kmph, hence, the net speed is 8 kmph.
28. Vinay fires two bullets from the same place at an interval of 12 minutes but Raju sitting in a train approaching the place hears the second report 11 minutes 30 seconds after the first. What is the approximate speed of the train (if sound travels at the speed of 330 metres per second)?
Solution:-?
29. Two trains A and B start simultaneously in the opposite direction from two points A and B and arrive at their destinations 9 and 4 hours respectively after their meeting each other. At what rate does the second train B travel if the first train travels at 80 km per hour.
Solution:- . ?
30. A railway passenger counts the telegraph poles on the railroad as he passes them. The telegraph poles are at a distance of 50 meters. What will be his count in 4 hours, if the speed of the train is 45 km per hour?
Solution:- In four hours, the train will travel 180 km (180,000 meters). The number of poles would be 180,000/50 = 3600.
31. A cyclist moving on a circular track of radius of 100 meters completes one revolution in 2 minutes. What is the average speed of cyclist?
Solution:- The length of the circular track would be equal to the circumference of the circle. In 2 minutes thus, the cyclist covers 3.14 ¥ 200 = 628 meters (using the formula for the circumference of a circle). Thus, the cyclist’s speed would be 628/2 = 314 meters/minute
32. A person traveled a distance of 200 kilometer between two cities by a car covering the first quarter of the journey at a constant speed of 40 km/h and the remaining three quarters at a constant speed of x km/h. If the average speed of the person for the entire journey was 53.33 km/h what is the value of x?
Solution:-?
33 . A car travels 1/3 of the distance on a straight road with a velocity of 10 km/h, the next 1/3 with a velocity of 20 km/h, and the last 1/3 with a velocity of 60 km/h. What is the average velocity of the car for the whole journey?
Solution:-. Assume a distance of 60 km in each stretch. Get the average speed by the formula. Total distance/ Total time = 180/10 = 18 kmph
34. Two cars started simultaneously toward each other from town A and B, that is 480 km apart. It took the first car traveling from A to B 8 hours to cover the distance and the second car traveling from B to A 12 hours. Determine at what distance from A the two cars meet.
Solution:-. The speed of the first car would be 60 kmph while the speed of the second car would be 40 kmph. The relative speed of the two cars would be 100 kmph. To cover 480 km they would take 480/100 = 4.8 hours -> In 4.8 hours, the car traveling from A to B would have traveled 4.8 x 60 = 288 km.
35. Walking at 3/4 of his usual speed, a man is 16 minutes late for his office. The usual time is taken by him to cover that distance is?
Solution:- At 3/4th speed, extra time = 1/3rd of time = 16 minutes. Normal time = 48 minutes.
36 . A and B travel the same distance at the rate of 8 kilometer and 10 kilometer an hour respectively. If A takes 30 minutes longer than B, the distance traveled by B is
Solution:- Solve using options. The value in option (C) fits the situation as 20/8 – 20/10 = 2.5 – 2 = 0.5 hours = 30 minutes.
37. Two trains for Patna leave Delhi at 6 a.m. and 6:45 a.m. and travel at 98 kmph and 136 kmph respectively. How many kilometers from Delhi will the two trains meet?
Solution:-?
38. Two trains A and B start from station X to Y, Y to X respectively. After passing each other, they take 12 hours and 3 hours to reach Y and X respectively. If train A is moving at the speed of 48 km/h, the speed of train B is?
Solution:-?
39. X and Y are two stations 600 km apart. A train starts from X and moves towards Y at the rate of 25 km/h.Another train starts from Y at the rate of 35 km/h. How far from X they will cross each other?
Solution:-. The distance would get divided in the ratio of speeds (since time is constant). Thus, the distance ratio would be 5: 7 and required distance = 5/12 ¥ 600 = 250 km
40. A starts from a point that is on the circumference of a circle moves 600 meters in the North direction and then again moves 800 meters East and reaches a point diametrically opposite the starting point. Find the diameter of the circle?
Solution:-.The diameter of the circle would be given by the hypotenuse of the right triangle with legs of 600 and 800 respectively. Hence, the required diameter = 1000 meters.
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