BANK & INSURANCE (SPEED TIME AND DISTANCE) PART 2

Total Questions: 45

11. A train running at 30 km/hr. takes 24 seconds to cross a platform. It takes 8 seconds to pass a man walking towards it at 6 km/hr. What is the length of the train and of the platform respectively?

Correct Answer: (b) 80m and 120m
Solution:

Speed of the train relative to the man = 30 + 6 km/hr = 36 × 5/18 m/s ⇒ 10 m/s

Distance travelled by the train in 8 seconds at this relative speed = 8 × 10 = 80m
Length of the train = 80m
Speed of the train = 30 km/hr = 30 × 5/18 m/s
⇒ 25/3 m/s
distance travelled in 24 seconds = 24 × 25/3
⇒ 200m
This distance 200m covered is the sum of the length of the train and the length of the platform
Length of train + length of platform = 200m
Length of platform = 200 - 80
⇒ 120m
∴ The lengths of train and the platform are 80m and 120m respectively

12. A 500 m long train passes a platform and a pole in 40 seconds and 25 seconds respectively. Find the length of platform in metres and speed of train in km/hr.

Correct Answer: (e) 300m and 72 km/hr
Solution:Let the speed of train and length of platform be s m/s and d metres
Speed of Train = (Length of Train)/(Time Taken)
⇒ s = (500 m)/(25 Seconds)
⇒ s = 20 m/s
Then, Speed of Train = (Length of Train + Length of Platform)/(Time Taken)
⇒ 20 m/s = (500 m + d)/(40 seconds)
⇒ 500 + d = 20 × 40
⇒ d = 800 - 500
⇒ d = 300 m
Now, Speed of Train (in km/hr) = 20 m/s × (18/5)
⇒ 72 km/hr
∴ The length of platform is 300 m and the speed of train is 72 km/hr.

13. Janaki goes to temple at the speed 45 km/h, and she reaches 5 minutes early. Next day she goes at the speed of 60 km/h, and he reaches 30 minutes early. Find the distance between her house and temple.

Correct Answer: (a) 75 km 
Solution:Let the distance be ‘x’ km
Therefore time taken to cover ‘x’ km at 45 kmph = x/45 hr
Time taken to cover ‘x’ km at 60 kmph = x/60 hr
But it is given that the difference between two timings
= 30 - 5 = 25 min = 25/60 hr = 5/12
⇒ x/45 - x/60 = 5/12
⇒ (60x - 45x)/45 × 60 = 5/12
⇒ 15x/45 × 60 = 5/12
⇒ x = 5 × 45 × 60 / 12 × 15
⇒ x = 75 km
∴ Distance between home and temple is 75 km

14. The ratio of speed of a train and a car is 9 : 5. If the train of length 900 m long crosses a pole in 20 sec, then find the time in which car crosses another train of length 840 m and speed 65 m/sec travelling in the same direction.

Correct Answer: (b) 21 seconds 
Solution:

According to the question,
A 900 m long train crosses a pole in 20 sec.
Speed of 1st train = 900/20 = 45 m/sec
Let the ratio of speed of a train and a car is 9x : 5x
then,
9x = 45 m/sec
⇒ x = 5 m/sec
Hence, Speed of Car = 5x = 5 × 5 m/sec
Speed of Car = 25 m/sec

Now, a car crosses a train of length 840 m travelling in the same direction
⇒ 840/(65 - 25) = t
⇒ 840/40 = t
⇒ t = 21 sec
∴ The time taken by car is 21 seconds.

15. Two trains A and B are moving in the opposite direction with speed 80 km / h and 70 km / h respectively. Train A starts from point C at 9: 00 a.m. and train B starts from point D at 10 : 30 a.m. The distance between C and D is 600 km. Find the total time taken by train A till reaching at meeting point.

Correct Answer: (d) 4 hours 42 minutes
Solution:Distance travelled by train A from 9: 00 a.m. to 10:30 a.m. = 80 × 1.5
= 120 km
⇒ Remaining distance = 600 - 120 = 480 km
Relative speed = (80 + 70) = 150 km/h
⇒ Required time = 480/150
⇒ Time taken = 3 hours 12 minutes.
Initial time taken by train A when B was not running = 1.5 hours.
Total time = 4 hours 42 minutes

16. A man covered 450 km at the rate of 75 km/hr and 360 km at the speed of 80 km/hr and remaining 195 km at 60 km/hr find the average speed of the whole journey.

Correct Answer: (d) 804/11 km/hr
Solution:

Time taken to cover 450 km = 450/75 hours
⇒ 6 hours
Time taken to cover 360 km = 360/80 hours
⇒ 9/2 hours
Time taken to cover 195 km = 195/60 hours
⇒ 13/4 hours
Now, Total time taken = [6 + (9/2) + (13/4)] hours
⇒ Total time taken = 55/4 hours
And, Total distance covered = (450 + 360 + 195) km
⇒ Total distance covered = 1005 km
And, Average speed = Total distance covered/Total time taken
⇒ Average speed = 1005 ÷ (55/4) km/hr
⇒ 804/11 km/hr

17. A train can cross a pole in 45 seconds. The speed of the train is 72 km/h. If the speed of the train is 54 km/h, then how much time will it take to cross pole by the train?

Correct Answer: (c) 60 sec
Solution:The speed of the train in m/sec = 72 × (5/18)
= 20 m/sec
Now the distance covered by train in 45 sec = 20 × 45 = 900 m.
Thus, the length of train = 900 m.
Now, the speed of train = 54 × (5/18) = 15 m/sec.
So, the time is taken by train to cross pole = 900/15
= 60 sec.
∴ Now the train crosses a pole in 60 sec.

18. Train A crosses a standing man at a speed of 15 m/s in ‘x’ seconds while train B crosses a platform of 200 m length in ‘3x’ seconds with a speed of 15 m/s. Length of train B is one-third the length of train A. Find the length of train B.

Correct Answer: (c) 25 m
Solution:Let the length of the train is ‘a’ meters.
⇒ a = 15 × x …(1)
According to question:
⇒ 3x = [200 + (a/3)]/15
⇒ 3x = [600 + a]/45
⇒ 135x = 600 + a
⇒ 135x - 600 = a …(2)
From (1) and (2)
135x - 600 = 15x
⇒ 120x = 600
⇒ x = 5 seconds
⇒ a = 15 × 5 = 75 meters
∴ Length of train B is 25 meters (i.e. 75/3)

19. A goods train of length 400 m moving at a speed of 90 kmph crosses a platform of a certain length in 22 seconds. Another train of length 350 m crosses the same platform in 25 seconds. Find the relative speed of both trains if they both travel in the same direction.

Correct Answer: (e) 18 kmph
Solution:Let the length of platform be A m.
⇒ (400 + A)/25 = 22
⇒ A = 150m
Let the speed of other train be B m/s.
⇒ (350 + 150)/25 = B
⇒ B = 20 m/s
∴ Relative speed of both trains when they are moving in the same direction = 25 - 20
= 5 m/s = 5 × 18/5 = 18 kmph

20. Time taken by two trains running in opposite directions to cross a man standing on the platform are 24 seconds and 10 seconds respectively. It took 16 seconds for the trains to cross each other. What is the ratio of their speeds?

Correct Answer: (c) 3 : 4
Solution:

Let the speed one train be u and the speed of the second train be v

Length of the first train = Speed × Time = 24u
Length of second train = Speed × Time = 10v
So, the time taken by both the trains to cross each other = {(24u + 10v)/(u + v)} = 16
⇒ 24u + 10v = 16u + 16v
⇒ 8u = 6v
⇒ u/v = 6/8 = 3/4
Therefore, u:v = 3:4