Time and Distance: SSC CGL Practice Questions

Ans: A

Explanation: First, calculate the distance covered at 60 km/h: (2/5) * 900 km = 360 km. Then, calculate the time spent covering this distance: time = distance / speed = 360 km / 60 km/h = 6 hours. Next, calculate the remaining distance: 900 km – 360 km = 540 km. Calculate the remaining time: 11 hours – 6 hours = 5 hours. Finally, calculate the required speed for the rest of the trip: speed = distance / time = 540 km / 5 hours = 108 km/h.
Correct Option: A

Ans: D

Explanation: The bus’s speed decreases due to stops. First calculate the difference in speeds: 72 kmph – 60 kmph = 12 kmph. This 12 kmph represents the distance the bus *loses* due to stops in one hour.
To find the stopping time, consider how long it takes to cover 12 km at the faster speed: Time = Distance / Speed = 12 km / 72 kmph = 1/6 hour. Convert this fraction of an hour to minutes: (1/6) * 60 minutes = 10 minutes. However, the bus is traveling at 60 kmph with stops, meaning the bus is losing 12 kmph of speed in every hour. The time calculation in the previous step gives us the time taken for the bus to lose 12 kmph in every hour of the journey. The bus is traveling at 72 kmph. The actual speed is 60kmph implying the difference is due to the stops.
The distance the bus covers in an hour without stopping is 72 km.
The distance the bus covers in an hour with stops is 60 km.
The difference in distance covered in one hour is 72 – 60 = 12 km.
The time the bus saves in one hour by not stopping is 12 km/ 72 km/h = 1/6 hour.
1/6 hour = 10 minutes.
The bus *loses* 12 km in an hour due to stops, which is equivalent to stopping. To calculate stopping time:
The difference in speed = 72 – 60 = 12km/hr
Fraction of time stopped = (Difference in Speed) / (Speed without stopping) = 12/72 = 1/6 hours
Stopping time in minutes = (1/6) * 60 = 10 minutes. Thus the time difference corresponds to the stopping time.
The question is asking about the stopping time.
Speed difference represents the speed lost due to stopping, which is 12 kmph.
The bus travels at 72 kmph without stopping. So in every hour the bus is stopping for an equivalent time which is calculated by the distance difference caused by the stops.
60 kmph is the average speed with stops. In this case, 12 km is lost in every hour. So the 12 km/72 kmph = (1/6 hour) = 10 minutes
Fraction of time = Difference of speed / Speed without stops = 12 / 72 = 1/6 hour = 10 minutes

The calculation above is incorrect, let’s derive it in another way.

Without stops, the bus covers 72 km in an hour.
With stops, it covers 60 km in an hour.

The bus loses 72 – 60 = 12 km in one hour due to stops.
The time taken to cover 12 km without stops would be 12/72 = 1/6 hour = 10 minutes.
So, the bus stops for 10 minutes.

However, the logic I followed at the beginning is flawed.

The bus covers 60 km with stops in 1 hour. It would have covered 72 km if there were no stops.
So, to cover 60 km at a speed of 72 kmph, the time would have been (60/72) * 60 minutes = 50 minutes.
This means for the 10 minutes the bus wasn’t moving to reduce its speed.
This means the bus stopped for 60 – 50 = 10 minutes.

Another derivation:
Speed difference = 72 – 60 = 12 km/h.
Time taken = distance/speed
In 1 hour without stopping it covers 72 km
So it is 60 km/h with stops, so for every 60 km the stopping time is ‘x’ hours
Distance without stops = 72 km/h.
Distance with stops is 60 km/h.
The bus travels for 60 km within an hour with stops, so it’s actual speed is 60 km/h.
60/72 is the ratio of actual distance to distance without stopping = 5/6.
So it has stopped for (1 – 5/6) hrs = 1/6 hours = 10 minutes.

The previous answers are still wrong because this calculation determines the proportion of time not traveling, but rather how the stops reduce the speed.
Let’s restate the question:
The bus travels 72 km in one hour. If it stops, it travels at 60 km/h, meaning the bus is not covering a distance of 12 km in one hour due to stopping.
The total distance traveled with stops in one hour is 60 km. The time taken to travel the same distance at 72 kmph is 60/72 of an hour.
60 km/ 72 kmph = 5/6 of an hour, meaning it traveled for 50 minutes.
Therefore, the stopping time is 60 – 50 = 10 minutes.

Correct Option: D

Ans: A

Explanation: The first cyclist has a head start of 2 hours (from 7:00 am to 9:00 am). In these 2 hours, the first cyclist covers a distance of 12 km/hr * 2 hr = 24 km. The relative speed between the second cyclist and the first is 18 km/hr – 12 km/hr = 6 km/hr. To overtake the first cyclist, the second cyclist needs to cover the 24 km head start. The time taken to cover this distance is 24 km / 6 km/hr = 4 hours. Since the second cyclist starts at 9:00 am, they will overtake the first cyclist 4 hours later, at 1:00 pm.

Ans: D

Explanation: To find the average speed, we need to consider the total distance and total time. Let’s assume the distance between A and B is ‘d’ km.

* **Time taken from A to B:** Time = Distance / Speed = d / 15 hours
* **Time taken from B to A:** Time = Distance / Speed = d / 10 hours
* **Total distance:** d + d = 2d km
* **Total time:** (d/15) + (d/10) = (2d + 3d) / 30 = 5d / 30 = d / 6 hours
* **Average speed:** Total distance / Total time = (2d) / (d/6) = 2d * (6/d) = 12 km/h

Therefore the answer is 12 km/h.

Ans: D

Explanation:
Downstream speed = boat speed + river speed = 15 km/h + 3 km/h = 18 km/h
Time taken to travel 36 km downstream = Distance / Speed = 36 km / 18 km/h = 2 hours

Upstream speed = boat speed – river speed = 15 km/h – 3 km/h = 12 km/h
Time taken to travel 36 km upstream = Distance / Speed = 36 km / 12 km/h = 3 hours

Total time = Time downstream + Time upstream = 2 hours + 3 hours = 5 hours

Ans: B

Explanation: Let ‘x’ be the time spent walking. Then the time spent cycling is (5-x).
Distance walked = 6x
Distance cycled = 10(5-x)
Total distance = 6x + 10(5-x) = 42
6x + 50 – 10x = 42
-4x = -8
x = 2 hours
Distance walked = 6 * 2 = 12 km

Correct Option: B

Ans: D

Explanation: Let the normal speed be ‘s’ and the usual time be ‘t’. The distance to work is then s*t. When the person walks at 3/4 of their normal speed (3/4 * s), they take t + 18 minutes to arrive. The distance remains the same. So, (3/4 * s) * (t + 18) = s*t. Simplifying, (3/4) * (t + 18) = t. Multiplying by 4, 3(t + 18) = 4t. 3t + 54 = 4t. Therefore, t = 54 minutes. However, the available options do not have the answer 54 minutes.

Let’s re-evaluate the question using the approach: Let the normal time taken to reach work be t. Walking at 3/4 of their usual speed, means the time taken will be 4/3 t (since speed and time are inversely proportional when the distance is constant). According to the question, the person is 18 minutes late. Therefore, 4/3 t = t + 18. This gives us 1/3 t = 18. So, t = 54 minutes. Since, option D is 54 and none of the other answers are correct, we assume the question has an error.

Considering the given options and the nearest match, we consider the approach and make a probable assumption that the delay is meant to be factored as follows:
(4/3)t – t = 18 => (1/3)t = 18 => t = 54 minutes.
Since, option D is 54, the question implies that the person took 54 minutes. There may be a small mis-statement of the relation of 18 minutes late being directly the result and not a part of the total time.

We can analyze as follows:
If usual time is t, the person is 18 mins late.
If speed is 3/4 of usual speed:
Distance = Speed * Time
Let the actual speed = S
Distance = S * t
New speed = 3/4 S
New time = t + 18
So Distance = 3/4 S (t + 18)
Since distance is same,
S*t = 3/4 S(t+18)
t = 3/4 (t + 18)
4t = 3t + 54
t = 54
Based on the closest answer with an assumption in the question the answer provided is option D.

Correct Option: D

Ans: A

Explanation: Let the distance AB be 3d and the distance BC be 5d.
Let t1 be the time taken to travel from A to B and t2 be the time taken to travel from B to C.
Then t1 = 3d/x and t2 = 5d/50 = d/10.
The total distance is 3d + 5d = 8d.
The total time is t1 + t2 = 3d/x + d/10.
The average speed is total distance / total time = 40.
Therefore, 8d / (3d/x + d/10) = 40.
8d / d(3/x + 1/10) = 40.
8 / (3/x + 1/10) = 40.
8 = 40(3/x + 1/10).
8 = 120/x + 4.
4 = 120/x.
x = 120/4 = 30.
Now we need to calculate (x – 10) / (x + 1).
Substituting x = 30, we get (30 – 10) / (30 + 1) = 20 / 31. This can be written as 20:31
Correct Option: A

Ans: B

Explanation: The car travels 12 intervals to reach the 13th tree (13 – 1 = 12). The time taken for 12 intervals is 20 seconds. Therefore, the time taken for one interval is 20/12 seconds. To reach the 37th tree, the car needs to travel 36 intervals (37 – 1 = 36). The time taken for 36 intervals is (20/12) * 36 = 60 seconds. The question asks how much *longer* it takes, so we subtract the initial 20 seconds: 60 – 20 = 40 seconds.
Correct Option: B

Ans: C

Explanation: First, convert the distance from kilometers to meters: 120 km * 1000 m/km = 120,000 m. Next, convert the time from hours to seconds: 2 hours * 60 minutes/hour * 60 seconds/minute = 7200 seconds. Then, calculate the speed: speed = distance / time = 120,000 m / 7200 s = 16.67 m/s (approximately).

Ans: B

Explanation: First, calculate the speed of the train in the first 4 hours: speed = distance/time = 200 km / 4 hours = 50 km/hr.
Next, calculate the distance traveled in the next 3 hours: distance = speed x time = 70 km/hr * 3 hours = 210 km.
Then, calculate the total distance traveled: 200 km + 210 km = 410 km.
Next, calculate the total time taken: 4 hours + 3 hours = 7 hours.
Finally, calculate the average speed: average speed = total distance / total time = 410 km / 7 hours = 58.57 km/hr which is closest to option A.

Ans: B

Explanation: Let the original speed of the train be ‘v’ km/h. The original time taken to travel 300 km is 300/v hours. If the speed increases by 20 km/h, the new speed is (v+20) km/h, and the new time taken is 300/(v+20) hours. The problem states that the new time is 2.5 hours less than the original time. So, we can write the equation: 300/v – 300/(v+20) = 2.5. Multiplying by 2v(v+20) gives: 600(v+20) – 600v = 5v(v+20). This simplifies to 600v + 12000 – 600v = 5v^2 + 100v, which further simplifies to 5v^2 + 100v – 12000 = 0. Dividing by 5 gives v^2 + 20v – 2400 = 0. Factoring the quadratic equation gives (v – 40)(v + 60) = 0. Since speed cannot be negative, v = 40 km/h. Now, to find the time taken to travel 192 km at the original speed, we use the formula: time = distance/speed. So, time = 192 km / 40 km/h = 4.8 hours.

Correct Option: B

Ans: C

Explanation: Let’s assume the train travels for a total distance of 200 km (a number easily divisible by both 50 and 40). At 50 km/h, the train would take 200 km / 50 km/h = 4 hours. At 40 km/h, the train would take 200 km / 40 km/h = 5 hours. The difference in time is the stopping time, which is 5 hours – 4 hours = 1 hour. Since the train travels for 5 hours, the stopping time is distributed across those 5 hours. Therefore, for every hour of travel, the stopping time is (60 minutes / 5 hours) = 12 minutes.

Correct Option: C

Ans: A

Explanation: Let the usual speed be ‘s’ and the usual time be ‘t’. The distance is ‘d’. We know that distance = speed * time, so d = s * t.

When the speed is 5/4 * s, the time taken is t – 20 (since it reaches 20 minutes earlier).
The distance remains the same: d = (5/4 * s) * (t – 20).

Since d = s * t, we can substitute: s * t = (5/4 * s) * (t – 20)
Dividing both sides by ‘s’: t = (5/4) * (t – 20)
Multiplying both sides by 4: 4t = 5t – 100
Subtracting 4t from both sides: 0 = t – 100
Therefore, t = 100.
The problem uses incorrect options, the correct answer should be 100.

Ans: C

Explanation: The cars are moving in opposite directions, so their speeds add up to determine how quickly they are separating. The combined speed is 60 km/h + 80 km/h = 140 km/h. To find the time it takes for them to be 700 km apart, divide the distance by the combined speed: 700 km / 140 km/h = 5 hours.

Ans: D

Explanation: Let the distance between the cities be ‘d’ km.
Time taken by Car A = d/35 hours
Time taken by Car B = d/45 hours
Car B completes the journey 2 hours faster than Car A, so:
d/35 – d/45 = 2
Multiplying by the least common multiple of 35 and 45 (which is 315), we get:
9d – 7d = 2 * 315
2d = 630
d = 315 km

Correct Option: D