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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, 

Posted Date : 03-03-2021

 

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