Quantitative Apptitude - Time & Distance Online Test 1

Explanation
To find the speed in km per hour, we need to convert the distance from meters to kilometers and the time from minutes to hours. Since there are 1000 meters in a kilometer and 60 minutes in an hour, the person's speed is calculated as 600 meters / 1000 meters per kilometer * 1 hour / 5 minutes * 60 minutes per hour = 7.2 km/h.

Explanation
Aditya's speed is given in km/hr, but the distance is given in meters. To calculate the time taken, we need to convert the speed from km/hr to m/min. Since 1 km = 1000 m and 1 hr = 60 min, we can convert the speed to m/min by multiplying it by 1000/60. So, Aditya's speed in m/min is (20 * 1000) / 60 = 333.33 m/min. To find the time taken, we divide the distance by the speed: 400 m / 333.33 m/min = 1.2 min. This can be simplified to 6/5. Therefore, Aditya takes 6/5 minutes to cover a distance of 400 m.

Explanation
In order to find the distance covered in 2 minutes, we need to convert the speed from km/h to m/min. Since 1 km = 1000 m and 1 hour = 60 minutes, we can convert the speed to m/min by multiplying it by 1000/60. Therefore, the person covers a distance of (72 * 1000/60) = 1200 meters in 1 minute. In 2 minutes, the person would cover a distance of 1200 * 2 = 2400 meters.

Explanation
After 1 hour, Liza would have run 1 mile per second for 3600 seconds, resulting in a total distance of 3600 miles. Tamar, on the other hand, would have run 2 miles per second for 3600 seconds, resulting in a total distance of 7200 miles. Therefore, the distance between them after 1 hour would be the difference between their distances, which is 7200 - 3600 = 3600 miles.

Explanation
To calculate the speed in km per hour, we need to convert the distance from meters to kilometers and the time from minutes to hours. Since there are 1000 meters in a kilometer and 60 minutes in an hour, the person's speed is calculated as follows: 600m / 1000m/km = 0.6 km and 5 minutes / 60 minutes/hour = 0.0833 hours. Dividing the distance by the time gives us 0.6 km / 0.0833 hours = 7.2 km/hour. Therefore, the person's speed is 7.2 km per hour.

Explanation
The train initially covers a distance in 50 minutes at a speed of 48 kmph. To reduce the time of the journey to 40 minutes, the train must increase its speed. By using the formula Speed = Distance/Time, we can calculate the new speed. The distance remains the same, so we can substitute the values into the formula: 48 kmph = Distance/50 min. Solving for the distance, we get: Distance = 48 kmph * 50 min = 2400 km. Now, we can calculate the new speed using the formula: Speed = Distance/Time = 2400 km/40 min = 60 kmph. Therefore, the speed at which the train must run to reduce the time of the journey to 40 minutes is 60 kmph.

Explanation
To find the speed required to cover the same distance in 1 hour, we can use the formula: Speed = Distance/Time.
Given that the distance is constant, we can assume it to be "d".
In the first scenario, the plane covers the distance in 5 hours at a speed of 240 kmph. So, the distance is 240 * 5 = 1200 km.
To cover the same distance in 1 hour, the speed will be 1200 km/1 hour = 1200 kmph.
Therefore, the correct answer is 1200 kmph, which is equivalent to 720 kmph.

Explanation
The cyclist covers a distance of 750m in 2 minutes and 30 seconds, which is equivalent to 2.5 minutes. To calculate the speed in km/hr, we need to convert the distance to kilometers and the time to hours. There are 1000 meters in 1 kilometer, so the distance is 0.75 kilometers. There are 60 minutes in 1 hour, so the time is 0.0417 hours. Dividing the distance by the time, we get a speed of approximately 18 km/hr.

Explanation
The trains take 1 minute to cross each other when traveling in the same direction, which means they cover a distance equal to the sum of their lengths in 1 minute. The total distance covered is 200 + 160 = 360 meters. Since they cover this distance in 1 minute, their combined speed is 360 meters per minute.

When the trains cross in opposite directions, they cover the same distance (360 meters) in only 10 seconds. To convert this to minutes, we divide by 60: 10/60 = 1/6 minute. Therefore, their combined speed when traveling in opposite directions is 360 meters per 1/6 minute.

To find the individual speeds of the trains, we need to subtract their lengths from the total distance covered.

In the same direction: 360 - 200 = 160 meters per minute, which is equivalent to 160/60 = 8/3 meters per second.

In opposite directions: 360 - 160 = 200 meters per 1/6 minute, which is equivalent to 200/(1/6) = 1200 meters per minute, or 1200/60 = 20 meters per second.

Therefore, the speeds of the trains are 8/3 m/s and 20 m/s, which can be approximated to 2.67 m/s and 20 m/s respectively.