BANK & INSURANCE (SPEED TIME AND DISTANCE) PART 1

Total Questions: 45

1. Two metro trains 150m long are moving in opposite directions. They cross each other in 15 seconds. If one is moving thrice as fast as the other, what is the speed of the faster metro train?

Correct Answer: (b) 54km/hr. 
Solution:Total speed of both the trains = (150m+150m)/15 = 20 m/s
Let speed of slower train = x km/hr.
Speed of faster train = 3x km/hr.
x + 3x = 20
4x = 20
x = 5
Speed of slower train = x = 5 m/s
Speed of faster train = 3x = 15 m/s = 54 km/hr.

2. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

Correct Answer: (c) 1 hour 15 minutes
Solution:Rate downstream = 1/10 × 60 = 6 km/h
Rate upstream = 2 km/h
Speed in still water = 1/2 (6 + 2) = 4 km/h
Required time = 5/4 hrs = 1 hour 15 minutes.

3. Two trains start from station A and B and travel towards each other at speeds of 50km/hr and 60km/hr respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is:-

Correct Answer: (b) 1320km 
Solution:

10 km/hr more speed has led to difference of 120 km
1 km/hr speed will lead to distance of 12 km.
Distance travelled at 110 km/hr.
So, distance = 110 × 12 = 1320 km.

4. A person travels from P to Q at a speed of 40 km/h and returns to P by increasing his speed by 50%. What is his average speed for both the trips?

Correct Answer: (c) 48 km/h
Solution:Speed from P to Q = 40 km/h
Speed from Q to P = 1.5 × 40 = 60 km/h
So, Average speed = (2 × 40 × 60)/100 = 48 km/h.

5. A boat running downstream covers 30 km in 6 hours, while for covering the same distance upstream it takes 10 hours. What is the speed of the boat in still water?

Correct Answer: (d) 4 km/hr. 
Solution:

Speed downstream = 30/6 = 5 km/hr.
Speed upstream = 30/10 = 3 km/hr.
Speed of the boat in still water = ½ (5 + 3) = 4 km/hr.

6. A man can row 10 kmph in still water and finds that it takes 4 times more to row up than to row down the same distance in the river. What is the speed of the current?

Correct Answer: (c) 20/3 km/hr. 
Solution:

Let the distance be d kms
Speed of the current be x km/ph
d/(10 – x) = 5d/(10 + x)
Solving for x, we get x = 20/3 km/hr.

7. Prerna starts from Place A at 5 am at constant speed of 50 km/h. She halts at Place B for half an hour and then drives at 30 km/h. If she reaches Place C at 8:30 am, which is 100 km away from Place A, how far is Place A from Place B?

Correct Answer: (d) 25 km 
Solution:Prerna travels only for 3 hour, since half an hour she halts at Place B.
Let the time for which she travels at 50 km/h be x hours, therefore she travels at 30 km/h for (3 – x) hours.
Now A to C,
50x + 30(3 – x) = 100
Solving, we get x = ½
So, Prerna travels for half an hour @ 50 km/h from Place A to B. Therefore, distance between A and B = ½ × 50 = 25 kms.

8. A train of length 200m, travelling at 80 km/h, overtook a motorcyclist travelling in the same direction at a speed of 20 km/h at 11:00 am. At 1:00 pm, it overtook another cyclist travelling in the same direction at a speed of 10 km/h. At what time will the motorcyclist overtake the cyclist?

Correct Answer: (a) 1:00 am 
Solution:In two hours the gap between the motorcycle and cycle = 80 × 2 – 20 × 2 = 120 kms.
So, there is a distance of 120 kms between motorcycle and cycle at 1:00 pm.
Now, they would meet in 120/(20 – 10) = 12 hours or at 1:00 am

9. The distance between Gwalior and Delhi is 800 kms. Rajdhani Express starts from Delhi at 80km/h. 60 minutes later Gwalior express leaves Gwalior for Delhi on the parallel tracks at 40km/h. How far from Gwalior will they cross each other?

Correct Answer: (c) 240 km
Solution:

In 60 minutes Rajdhani express can cover 80km. So, the rest distance is 720 Km which will be jointly covered by both the trains.
Time Taken = 720/(80 + 40) = 6 Hours
Distance from Gwalior is 6 × 40 = 240 km.

10. Ray starts from A and Kamal starts from B to meet each other. Speed of Ray is 15 kilometer per hour, while speed of Kamal is 10 kilometer per hour. If the distance between A and B is 150 kilometers and both Ray and Kamal start the journey at the same time, in how much time will they meet?

Correct Answer: (a) 6 hours 
Solution:Effective speed = 15 + 10 = 25 km/hr
Distance = 150 km
Time taken = 150/25 = 6 hours