Time and Distance: Bank Exam Practice Questions (SBI, IBPS, RRB, PO & Clerk)

Ans: E

Explanation: Let the speed of the boat in still water be ‘b’ kmph and the speed of the stream be ‘s’ kmph.
Upstream speed = b – s = 6 kmph.
Time taken upstream = Distance / Speed = 30 / 6 = 5 hours.
Total time for the journey is 8 hours.
Time taken downstream = 8 – 5 = 3 hours.
Downstream speed = Distance / Time = 30 / 3 = 10 kmph.
Since b – s = 6 and b + s = 10,
Adding the equations: 2b = 16 => b = 8
Substituting b in b + s = 10, 8 + s = 10 => s = 2
The boat’s downstream speed is 10 kmph.
Time to travel 50 km downstream = Distance / Speed = 50 / 10 = 5 hours.

Correct Option: E

Ans: A

Explanation: First, convert the time to hours: 84 minutes = 84/60 = 1.4 hours. The speed against the current is distance/time = 14 km / 1.4 hours = 10 km/h. Let the boat’s speed in calm water be ‘b’. When the boat travels against the current, the current’s speed (6 km/h) subtracts from the boat’s speed. So, b – 6 = 10. Therefore, b = 10 + 6 = 16 km/h.
Correct Option: A

Ans: E

Explanation: Let ‘x’ be the speed of the current.
Downstream speed = 15 + x km/h
Upstream speed = 15 – x km/h
Time taken downstream = 30 / (15 + x) hours
Time taken upstream = 30 / (15 – x) hours
Total time = 4.5 hours
So, 30 / (15 + x) + 30 / (15 – x) = 4.5
Multiplying by (15+x)(15-x):
30(15 – x) + 30(15 + x) = 4.5(225 – x^2)
450 – 30x + 450 + 30x = 1012.5 – 4.5x^2
900 = 1012.5 – 4.5x^2
4. 5x^2 = 112.5
x^2 = 25
x = 5 km/h

Ans: D

Explanation: Let the speed of the stream be ‘x’ km/hr.
Upstream speed = (15 – x) km/hr
Downstream speed = (15 + x) km/hr

Time taken upstream = Distance / Speed = 48 / (15 – x)
Time taken downstream = Distance / Speed = 72 / (15 + x)

Given that the time taken upstream is equal to the time taken downstream:
48 / (15 – x) = 72 / (15 + x)

Cross-multiply:
48 * (15 + x) = 72 * (15 – x)
720 + 48x = 1080 – 72x
120x = 360
x = 360 / 120
x = 3 km/hr

Ans: C

Explanation: Let the speed of the boat in still water be ‘b’ km/hr, and the speed of the current be ‘c’ km/hr.

When the boat travels against the current (upstream):
Speed = b – c
Distance = 8 km
Time = 2 hours
Therefore, b – c = 8/2 = 4 (Equation 1)

When the boat travels with the current (downstream):
Speed = b + c
Distance = 12 km
Time = 1.5 hours
Therefore, b + c = 12/1.5 = 8 (Equation 2)

Adding Equation 1 and Equation 2:
(b – c) + (b + c) = 4 + 8
2b = 12
b = 6 km/hr

Substituting b = 6 in Equation 2:
6 + c = 8
c = 8 – 6 = 2 km/hr

Therefore, the speed of the current is 2 km/hr.

Correct Option: C

Ans: A

Explanation: Let the stream’s speed be ‘x’ km/hr. Then the boat’s speed in still water is 5x km/hr.
Downstream speed = boat’s speed + stream’s speed = 5x + x = 6x km/hr.
Given, downstream speed is 24 km/hr. Therefore, 6x = 24, which gives x = 4 km/hr (stream’s speed).
Boat’s speed in still water = 5x = 5 * 4 = 20 km/hr.
Upstream speed = boat’s speed – stream’s speed = 20 – 4 = 16 km/hr.
Time taken to travel 48 km upstream = distance / upstream speed = 48 / 16 = 3 hours.

Correct Option: A

Ans: D

Explanation: Let the time taken to travel downstream be ‘t’ hours. Then the time taken to travel upstream is 1.6667t hours (66.67% more).

Downstream speed = boat speed + stream speed = (12 + x) kmph
Upstream speed = boat speed – stream speed = (12 – x) kmph

Distance = Speed x Time

Downstream: 270 = (12 + x) * t => t = 270 / (12 + x)
Upstream: 270 = (12 – x) * 1.6667t => 270 = (12 – x) * (1.6667 * (270 / (12 + x)))

Simplifying the upstream equation:
1 = (12 – x) * 1.6667 / (12 + x)
12 + x = 1.6667 * (12 – x)
12 + x = (5/3) * (12 – x)
36 + 3x = 5(12 – x)
36 + 3x = 60 – 5x
8x = 24
x = 3

Correct Option: D

Ans: D

Explanation:
1. Calculate the initial speed of the car: Speed = Distance / Time = 200 km / 5 hours = 40 km/hour.
2. Calculate the initial speed of the train: Speed = Distance / Time = 420 km / 7 hours = 60 km/hour.
3. Calculate the car’s new speed (20% increase): 40 km/hour * 0.20 = 8 km/hour increase. New speed = 40 + 8 = 48 km/hour.
4. Calculate the train’s new speed (30% increase): 60 km/hour * 0.30 = 18 km/hour increase. New speed = 60 + 18 = 78 km/hour.
5. Find the ratio of the new speeds (car : train): 48 : 78. Simplify the ratio by dividing both sides by their greatest common divisor, which is 6. 48/6 = 8 and 78/6 = 13.
6. The ratio is 8 : 13

Correct Option: D

Ans: B

Explanation:
1. **Calculate the time for the second segment:** The second segment takes 66.67% more time than the first (24 minutes). 66.67% is approximately 2/3. So, the second segment takes 24 + (2/3)*24 = 24 + 16 = 40 minutes.

2. **Calculate the time for the third segment:** The third segment takes 25% more time than the first (24 minutes). 25% is 1/4. So, the third segment takes 24 + (1/4)*24 = 24 + 6 = 30 minutes.

3. **Calculate the total time:** The total time is 24 + 40 + 30 = 94 minutes. Convert this to hours: 94 minutes / 60 minutes/hour = 1.5667 hours (approximately).

4. **Calculate the total distance:** The total distance is 180 km.

5. **Calculate the average speed:** Average speed = Total distance / Total time. Average speed = 180 km / 1.5667 hours = 114.89 km/h (approximately).

6. **Find the closest answer choice:** The closest answer choice is 115 km/h.

Correct Option: B

Ans: B

Explanation:
First calculate the time to travel 40 km without any rest.
Time = Distance / Speed = 40 km / 16 km/h = 2.5 hours = 2 hours and 30 minutes.

Next calculate the number of rest periods. The person rests after each kilometer, so for 40 kilometers he rests 39 times (he doesn’t rest at the end).
Total rest time = 39 rests * 4 minutes/rest = 156 minutes = 2 hours and 36 minutes.

Total time = Travel time + Rest time = 2 hours 30 minutes + 2 hours 36 minutes = 5 hours 6 minutes.

Correct Option: B

Ans: C

Explanation: Let the distance between P and Q be ‘d’. Let the speed of the swimmer in still water be ‘s’ and the speed of the current be ‘c’.
Downstream speed = s + c
Upstream speed = s – c
Time taken to swim from P to Q (downstream) = d / (s + c)
Time taken to swim from Q to P (upstream) = d / (s – c)
Given that the time taken downstream is one-third of the time taken upstream:
d / (s + c) = (1/3) * [d / (s – c)]
(s – c) = (1/3) * (s + c)
3(s – c) = s + c
3s – 3c = s + c
2s = 4c
s / c = 4 / 2 = 2 / 1
The ratio of the swimmer’s speed in still water to the speed of the current is 2:1.

Ans: E

Explanation: Let the length of the train be ‘x’ meters. The length of the platform is x/3 meters. The total distance covered by the train to completely pass the platform is the sum of the train’s length and the platform’s length, which is x + x/3 = 4x/3 meters. We know the speed of the train is 25 m/s and the time taken is 20 seconds. Therefore, distance = speed × time. So, 4x/3 = 25 × 20. 4x/3 = 500. Multiplying both sides by 3, we get 4x = 1500. Dividing both sides by 4, we get x = 375.

Correct Option: E

Ans: B

Explanation: First, convert the speed from km/h to m/s: 72 km/h * (1000 m/km) / (3600 s/h) = 20 m/s.

When the train crosses the lamp post, it covers its own length. Distance = speed * time, so the length of the train is 20 m/s * 10 s = 200 m.

When the train crosses the bridge, it covers the length of the bridge plus its own length. Let ‘b’ be the length of the bridge. The total distance is (200 + b) meters. The time taken is 30 seconds. So, 20 m/s * 30 s = 200 + b.
600 = 200 + b.
b = 600 – 200 = 400 m.

Ans: B

Explanation: Let the speeds of A, B, and the stream be 15x, 14x, and 10x respectively. The difference in the speeds of A and B is 15x – 14x = x. We are given this difference is 2 km/h, thus x = 2 km/h.
Speed of stream = 10x = 10 * 2 = 20 km/h
Speed of A downstream = 15x + 10x = 30x = 30 * 2 = 60 km/h
Speed of B upstream = 14x – 10x = 4x = 4 * 2 = 8 km/h
Time taken by A to travel 150 km downstream = 150 / 60 = 2.5 hours
Time taken by B to travel 120 km upstream = 120 / 8 = 15 hours
Time difference = 15 – 2.5 = 12.5 hours. However, since the stream speed is greater than the speed of boat B in the opposite direction, the boat B will not be able to move upstream. We should have calculated with the speed of stream against the boats, we should not have assumed that the stream speed can be added or substracted like that. Let the speeds of A, B, and stream be 15x, 14x and 10x.
Then A’s speed = 15x and B’s speed = 14x.
Given, 15x-14x = 2; hence x=2
A’s speed in still water = 15*2 = 30 km/h
B’s speed in still water = 14*2 = 28 km/h
Stream speed = 10*2 = 20 km/h
A’s downstream speed = 30+20=50 km/h
Time for A= 150/50=3 hours
B’s upstream speed = 28-20=8 km/h
Time for B = 120/8=15 hours
Time difference= 15-3 = 12 hours

Correct Option: B

Ans: A

Explanation:
1. **Convert Time to Hours:** The time taken is 1/5 minute, which is (1/5) / 60 = 1/300 hours.
2. **Convert Lengths to Kilometers:** The lengths of the trains are 210 meters and 270 meters, so the combined length is 210 + 270 = 480 meters, or 0.48 km.
3. **Combined Speed:** Let the speed of the first train be ‘x’ km/hr, and the second train be ‘x + 12’ km/hr. Their relative speed (since they are moving towards each other) is x + (x + 12) = 2x + 12 km/hr.
4. **Distance, Speed, and Time:** We know distance = speed * time. In this case, the distance is the combined length of the trains (0.48 km), the speed is the relative speed (2x + 12 km/hr), and the time is 1/300 hours.
5. **Set up the Equation:** So, 0.48 = (2x + 12) * (1/300).
6. **Solve for x:**
* 0.48 * 300 = 2x + 12
* 144 = 2x + 12
* 132 = 2x
* x = 66

Correct Option: A

Ans: A

Explanation: First, convert the speeds from km/hr to m/s:
Train 1: 54 km/hr = 54 * (1000 m / 3600 s) = 15 m/s
Train 2: 36 km/hr = 36 * (1000 m / 3600 s) = 10 m/s
Since the trains are traveling towards each other, their relative speed is the sum of their speeds: 15 m/s + 10 m/s = 25 m/s.
The total distance the trains need to cover to completely pass each other is the sum of their lengths: 120 m + 180 m = 300 m.
Time = Distance / Speed = 300 m / 25 m/s = 12 seconds.