T ime, Speed and Distance: Relative Motion, Trains

1. A journalist travelled 1200 km by air and this 3/5 th of his trip. What was the total distance (in km) of the complete trip?
a) 2000         b) 1500        c) 3000         d) 2500

2. A train moving at two-third of its normal speed reaches the destination half an hour late. What is the normal time taken?
a) 1.5 hrs        b) 1 hr         c) 2 hrs         d) 3 hrs

3. A train 150 m long takes 9 sec to cross a man walking at 8 kmph in a direction opposite to that of the train. Find the speed (in km/hr) of the train?
a) 72             b) 60            c) 54            d) 52

4. A train speeds past a pole in 15 sec and past a platform 100 m long in 30 sec. Find the length (in m) of the train?
a) 200           b) 100           c) 300           d) 150

5. A train can cover 520 km in 4 hours. If the speed is increased by 20 kmph, then how much time (in hr) does the train take to cover a distance of 900 km?
a) 4            b) 8            c) 6            d) 3

6. A train speeds past a pole in 8 sec and past a bridge 250 m long in 24 sec. Find the length of the train?
a) 95 m        b) 160 m      c) 125 m       d) 250 m

7. A 180 m long train crosses a man walking at a speed of 6 km/hr in opposite direction in 6 sec. The speed of the train is?
a) 85 km/hr        b) 102 km/hr         c) 96 km/hr          d) 119 km/hr

8. A girl rides her horse for 10 km at an average speed of 12 km/hr and for 12 km at an average speed of 10 km/hr. What is the average speed for the entire trip?
a) 1.44 km/hr         b) 5 km/hr       c) 10.8 km/hr            d) 11.9 km/hr

9. A train passes a man standing at the station in 5 sec and crosses a 240 m long platform in 25 sec. Calculate the length and the speed of the train.
a) 30 m, 6 m/sec      b) 40 m, 8 m/sec         c) 50 m, 10 m/sec           d) 60 m, 12 m/sec

10. A car travels 300 km at a uniform rate. If the speed of the car had been 5 km/hr more, the journey would have taken 2 hrs less. What is the speed of the car?
a) 20 km/hr           b) 25 km/hr           c) 30 km/hr         d) 60 km/hr

11. A train 200 m long is running at a speed of 64 kmph. In what time will it cross a man who is running at 8 kmph in the direction opposite to that in which the train is moving?
a) 7 sec.        b) 8 sec.        c) 9 sec.           d) 10 sec.

12. Sanjay and Samit can cover a distance of 660 m in 81 sec and 88 sec respectively. By how many sec will Samit win the race if he has a head start of 60 m?
a) 1          b) 2         c) 3            d) 4

13. A train takes 18 seconds to pass through a platform 162 m long and 15 seconds to pass through another platform 120 m long. The length of the train (in m) is....
a) 70             b) 80             c) 90           d) 105

14. A can run 2 km in 6 min 20 sec and B can cover the same distance in 6 min 40 sec. In a 2 km race, by what distance (in m) can A beat B?
a) 50         b) 100         c) 150         d) 200

15. A bus travels at 30 km/hr for 2 hr, 40 km/hr for 3 hr and the remaining distance at 60 km/hr. If the total distance to be covered is 300 km, then how much time did it take to complete the journey?
a) 5 hr          b) 7 hr           c) 10 hr          d) 14 hr

16. If a person has a speed of 40 km/hr, he reaches the office 5 min late and if he increases his speed to 50 km/hr, he reaches the office 3 min early. Calculate the distance to be covered.
a) 18 km            b) 26.6 km            c) 30 km           d) 36 km

17. Two men start at the same time from A and B and proceed towards each other at 6 m/sec and 8 m/sec respectively. When they met, it was found that one has travelled 20 m more than the other. Find the distance between A and B?
a) 60 m         b) 120 m           c) 130 m        d) 140 m

18. A train is moving at a speed of 108 km/hr. If the length of the train is 90 m, then how long will it take to cross a railway platform 120 m long?
a) 7 sec        b) 6 sec          c)12 sec           d) 9 sec

19. A man can row 22 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate at which stream is running?
a) 20 km/hr           b) 9 km/hr            c) 11 km/hr           d) 8 km/hr

20. A man can row 7 kmph in still water. If in a river running at 2 km an hour, it takes 56 minutes to row to a place and back, then how far is the place from the starting point?
a) 2 km           b) 7 km        c) 3 km          d) 9 km

Key With Explanations

2-b; Let the normal speed of the train be x and actual time taken be t.
Total distance = x t

3-d; Speed of train relative to man = (x + 8) kmph

Now, this is increased by 20 km/hr Hence, speed is 150 km/hr. At this speed time taken by the train to
cover  900 km = 900/150 = 6 hours

6-c; Let the length of the train be x.

⇒ 3x = x + 250 ⇒ x = 125 m

7-b; The speed of the man is

8-c;  Total distance covered = 10 + 12 = 22 km

9-d; Let the length of train be ‘x’
∴ Total distance while covering platform = x + 240
Total distance while passing man = x
Since the speed of the train remains the same

10-b; Let speed of the car be x km/hr.
Then, time taken to cover 300 km = 300/x

Time taken by the train to cross the man = time taken by it to cover 200 m at 20 m / sec
200/20 = 10 sec

12-a; Samit runs 660 m in 88 sec
∴ Samit runs (660 - 60) m in 88/660 × 600 sec
i.e. 80 sec. But Sanjay runs 660 m in 81 sec So, Samit wins by (81 - 80) sec, i.e. 1 sec.

13-c; Let the length of the train be x metres. When a train crosses a platform it covers a distance equal to the sum of lengths of train and platform. Also, the speed of train is same.

⇒ 6x + 720 = 5x + 810
⇒ 6x - 5x = 810 - 720
⇒ x = 90
∴ The length of the train = 90 m.

14-b; Clearly, A beats B by 20 sec.
Distance covered by B in 20 sec

∴ A beats B by 100 m.

15-b; Distance travelled by bus at the rate of 60 km/hr = 300 - 30 × 2 - 40 × 3 = 120 km
Time taken to cover 120 km at the speed of 60 km/hr = 2 hrs
Hence, total time taken = 2 + 3 + 2 = 7 hr

⇒ 8x = 6x + 120
⇒ 2x = 120
⇒ x = 60 m
∴ Distance between A and B = 60 + 60 + 20 = 140 m

18-a;  Speed of train = 108 × 5/18 = 30 m/sec
Distance covered in passing the platform = (90 + 120)= 210 m.
∴Time taken = 210/30 = 7 sec.

19-c; Let the speed of the man when rowing upstream be x kmph, then his speed downstream = 3x kmph.
∴ Rate in still water = 1/2 (3x + x) = 2x kmph
So, 2x = 22 ⇒ x = 11
∴ Rate upstream = 11 km/hr
Rate downstream = 33 km/hr
Hence, the rate of stream
= 1/2 (33 - 11) = 11 km/hr

20-c; Speed downstream = 7 + 2 = 9 kmph
Speed upstream = 7 - 2 = 5 kmph
Let the distance be x. Then,

Some more....

1. A train of length 700 m can cross a platform of length 500 m in 40 sec. Find the speed of the train in kmph.
A:  108 kmph

2. Two trains of lengths 250 m and 350 m are travelling at a speed of 41 kmph and 31 kmph respectively in opposite directions can cross each other in ........
A: 30 sec

3. A 300 m long train runs with a speed of 64 kmph and crosses a person, who travels in the opposite direction to the train in 15 sec. Find the speed of the man (in kmph).
A:  8

4. The ratio of lengths of two trains is 3 : 2. The speeds of the trains are 20 kmph and 30 kmph respectively. The time taken to cross each other, when they are travelling in opposite directions is 36 sec. Find the length of longer train.
A: 300

5. Train A can cross a tree in 30 sec and train B can cross the tree in 1 min 20 sec. The length of Train A is half of the length of Train B. Find the ratio of speeds of A and B.
A:  4 : 3

6. Two trains running in opposite directions can cross a man, who is standing on a platform in 52 sec and 38 sec respectively and both the trains can cross each other in 44 sec. Find the ratio of the speeds.
A:  3 : 4

7. Train A is running at a speed of 27.5 kmph and Train B is running at 7.5 kmph in the same direction. Train A completely passes a man sitting in the train B in 18 sec. What is the length of train A?
A: 100 m

8. The distance between Ongole and Tirupathi is 480 km. One train leaves Ongole to Tirupathi at 65 kmph and another leaves Tirupathi to Ongole at 55 kmph. Find the distance of the point where the two trains meet from Ongole and the time taken to meet each other.
A:  260 km, 4h

9. A train can cross two persons who are travelling at speeds of 3 kmph and 6 kmph in opposite direction to the train in 36 sec and 30 sec respectively. Find the length of the train.
A:  150 m

10. The distance between Vijayawada and Hyderabad is 500 km. One train at a speed of 50 kmph leaves Hyderabad at 9 A.M. to Vijayawada. Another train at a speed of 40 kmph leaves Vijayawada at 10 A.M. to
Hyderabad. Then at what time both trains meet?
A: 3:00 pm

11. A train can go 120 km in an hour without stoppages. The train can go 100 km in an hour with stoppages. What is the time in minutes for which train stops?
A: 10

12. The distance travelled by a train is 300 km. The speed of the train is one more than twice the time taken to travel the distance. What will be the respective ratio of the speed of train and time taken to travel.
A:  25 : 12

13. A train consists of 12 bogies (inclusive of the engine). Each bogie is 15 m long. The train crossed a telegraph post in 18 seconds. Due to some problem two bogies were detached. Moving at the same speed the train now crossed the telegraph post in?
A:   15 sec

14. Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite
direction?
A:   12

15. Train A moving uniformly, crosses a pole in 29 seconds and a platform in 59 seconds. The length of the platform is 240 meters What is the length of another train B whose length is equal to the sum of the three− fourth the length of the train A and half the length of the platform together?
A:   294 meters

16. Two identical trains A and B running in opposite direction at same speed take 2 min to cross each other completely. The number of bogies of A are increased from 12 to 16. How much more time would they now require to cross each other?
A:   20 sec

17. Two metro trains each 120 m long are moving in opposite directions. They cross each other in 12 seconds. If one is moving thrice as fast as the other, what is the speed of the faster metro train?
A: 54 km/ hr

18. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 60 kms away from A at the same time. On the way, however, the train lost about 15 minutes while stopping at the stations. The speed of the car is...
A: 80 km/ hr

Explanations

Posted Date : 15-04-2022

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.