BANK & INSURANCE (SPEED TIME AND DISTANCE) PART 2

Total Questions: 45

1. Two trains are of the same length. The first train crosses a pole in 30 seconds and train B crosses a platform in 40 seconds. But the speed of train B is 20 % more than the train A. Find out the ratio of the length of train and length of the platform.

Correct Answer: (d) 5 : 3 
Solution:

Given:
Train A crosses a pole in 30 seconds.
Train B crosses a platform in 40 seconds
Formula used:
Speed = Distance/Time

Calculation:
Let the speed of train A = s m/sec
⇒ Length of the train (L) = s × 30
⇒ L = 30s ⇒ L/30 = s
⇒ Let the length of the platform = P metre
⇒ s + 20% of s = (30s + P)/40
⇒ 120s/100 = (30s + P)/40
⇒ 4800s = 3000s + 100P
⇒ 1800s = 100P ⇒ s/P = 1/18
⇒ s = P/18
⇒ L/30 = P/18
⇒ L/P = 30/18 ⇒ L/P = 5/3
⇒ Required ratio = 5 : 3

2. A boat travels 8 km downstream from A to B in 20 minutes and thereafter travels 10 km upstream to reach point C. If the speed while travelling upstream is 3/4 of the downstream speed, find the average speed of the whole journey.

Correct Answer: (d) 81/4 km/hr 
Solution:

Given:
Boat travels 8 km downstream A to B in 20 minutes
Boat travels 10 km upstream to reach point C
Speed while upstream = 3/4 of the downstream speed

Concept used:
Downstream Speed = Speed of Boat + Speed of Stream
And, Upstream Speed = Speed of Boat - Speed of Stream

Calculation:
Let speed of Boat = x km/hr
And Speed of Stream = y km/hr
Downstream Speed = x + y
Upstream Speed = x - y

Boat travels 8 km downstream
Time taken = 20 minutes = 20/60 hour = 1/3 hour
Downstream Speed = Distance/Time taken
⇒ Downstream speed = 8 ÷ 1/3 = 24 km/hr

Upstream speed = 3/4 × Downstream speed
⇒ Upstream speed = 3/4 × 24 = 18 km/hr

Distance covered in Upstream from B to C = 10 km
Time taken to complete B to C = 10/18 hour = 5/9 hour

Total time taken = (1/3 + 5/9) = 8/9 hour
Total distance = (8 + 10) km = 18 km

Average Speed = Total distance / total time taken
⇒ Average speed = 18 ÷ 8/9 = 81/4 km/hr

The average Speed is 81/4 km/hr

3. Total distance of a journey is 250 km. X covered the first 20 km at a speed of 40 km/h, the next 140 km at 70 km/h, and the remaining journey at 18 km/h. Find the average speed to complete the journey.

Correct Answer: (a) 33.33 Km/hr 
Solution:

Given:
Total distance covered = 250 km
Speed in the first part of the journey = 40 km/h
Speed in the second part of the journey = 70 km/h
Speed in the third and final part of the journey = 18 km/h

Formula used:
Speed = Distance/Time
Average speed = Total distance / Total Time

Calculation:
Average speed = 250/((20/40) + (140/70) + (90/18))
= 250/[(1/2) + 2 + 5] = 250/(15/2) = (500/15)
= 33.33 km/h
∴ The average speed of the whole journey is 33.33 km/h.

4. The distance between two places is 100 km. A and B start towards each other at the same time and meet each other after 4 hours. If A travelled with double of his speed while B travelled with 2/3rd of his speed, they would have met after 3 hours 20 minutes. What is the speed of A?

Correct Answer: (c) 10 km/hr
Solution:

Given:
The distance between two places is 100 km.
The meet after 4 hours.
Formula Used:
Distance = Speed × Time

Calculation:
Let the speed of A be x.
Let the speed of B be y.
According to the question:
⇒ 100/(x + y) = 4
⇒ x + y = 25
⇒ y = 25 - x

The new speed of A = 2x
The new speed of B = 2y/3

⇒ 100/(2x + 2y/3) = 10/3
⇒ 2x + 2y/3 = 30
⇒ 2x + 2(25 - x)/3 = 30
⇒ 6x + 50 - 2x = 90
⇒ 4x = 40
⇒ x = 10 km/hr
∴ The speed of A is 10 km/hr.

5. The average speed of a bike is 7/9th of the average speed of the bus. The average speed of the bus is 80% more than the average speed of the car. Find the distance covered by the bike in 2 hours if car covers 750 km in 50 hours.

Correct Answer: (e) None of these
Solution:Average speed of the car = 750/50 = 15 km/hr
∴ Average speed = Total distance / Total time
Average speed of bus = 15 × (180/100) = 27 km/hr
Average speed of bike = 27 × 7/9 = 21 km/hr
∴ Distance covered by bike in 2 hours = 42 km.

6. A running train crosses a stationary pole in 4 seconds and a platform 75m long in 9 seconds. what will be the speed and length of the train respectively?

Correct Answer: (c) 54 km/hr and 60m
Solution:

Let the speed of the train = x km/hr
and the length of train = y m
x km/hr = 5x/18 m/s

case 1: pole
4 seconds = y/(5x/18)
18y = 20x
10x = 9y …(1)

case 2: platform
9 seconds = (y + 75)/(5x/18)
18(y+75) = 45x
2(y+75) = 5x
2y + 150 = 5x
4y + 300 = 10x
4y + 300 = 9y (from equation 1)
5y = 300 ⇒ y = 60m
∴ x = 9 × 60 / 10 = 54
∴ The speed and length of train is 54 km/hr and 60m respectively

7. The distance covered by B in 4 hours is 15 Km less than the distance covered by A in 5 hours. The distance covered by A in 3 hours is 15 Km less than the distance covered by B in 3 hours. If they start covering a distance of 195 km in the same direction, in what time will they cross?

Correct Answer: (c) 39
Solution:

Let a and b be the speed of A and B
According to the question,
5a - 4b = 15 …(1)
3b - 3a = 15 …(2)

Equation (1) = (2),
5a - 4b = 3b - 3a
5a + 3a = 3b + 4b
8a = 7b
Ratio of a to b is 7 : 8

let 7x and 8x be the speed of a and b
Put (3) in equation (1)
5 × (7x) - 4 × (8x) = 15
35x - 32x = 15
3x = 15
x = 5

Then,
Speed of A = 7x = 35 km/hr
Speed of B = 8x = 40 km/hr
Time taken to meet if both start travelling a distance of 195 km in same direction,
Time = 195/(40-35) = 195/5 = 39 hours.
∴ The correct answer is 39 hours.

8. The speed of a passenger train is 15 km/hr more than the speed of a goods train. If the passenger train takes 10 hour less than the goods train to cover 216 km; find the speed of passenger train.

Correct Answer: (c) 27 km/hr
Solution:Let the speed of passenger train be x km/hr
Then, the speed of goods train = (x - 15) km/hr
∴ Time taken by passenger train to cover the distance of 216 km = 216/x hr
And time taken by goods train to cover the same distance = 216/(x - 15) hr
∴ According to question,
216/(x - 15) - 216/x = 10
⇒ {216x - (x - 15)216} / x(x - 15) = 10
⇒ 216x - 216x + 3240 / x(x - 15) = 10
⇒ 324 = x(x - 15)
⇒ x² - 15x - 324 = 0
⇒ x² - 27x + 12x - 324 = 0
⇒ (x - 27)(x + 12) = 0
⇒ x = 27 or x = -12
∴ The speed of the passenger train is 27 km/hr

9. A train running at a speed of 72 km/h crosses a man standing near the railway line in 9 seconds. Find the time taken by the train to cross a platform of length 120 meters.

Correct Answer: (c) 15 sec
Solution:Speed = 72 × 5/18 = 20 m/s
The distance travelled to cross a man is equal to the length of the train.
∴ D = 20 × 9 = 180 m
Train’s length = 180 m
The distance travelled to cross a platform is equal to the length of the train + the length of platform.
∴ D = 180 + 120 = 300 m
T = 300/20 = 15 sec
∴ The answer is 15 sec.

10. A thief started running from point X at a speed of 20 km/hr, after running for 30 minutes, when he watched the police at the distance of 400 m coming from opposite direction at the speed of 30 km/hr, he turned and started running at 25 km/hr in the same direction as of police. After how much distance from point X police will catch the thief?

Correct Answer: (b) 8 m 
Solution:

Calculation:
In 20 minutes, thief covered the distance from point X = 20 × (30/60) km ⇒ 10 km
Relative speed of police with respect to thief = (30 - 25) km/hr ⇒ 5 km/hr
Time taken by police to cover 400 m or 0.4 km = 0.4/5 hr ⇒ 0.08 hr
Distance covered by the thief in 0.08 hr = 25 × 0.08 ⇒ 2 km
Distance from Point X = (10 - 2) km = 8 km
∴ Police will catch the thief at 8 km from point X.