Quantitative Apptitude - Time & Distance Online Test 4

Explanation
If a man is late by 5/2 hours while walking at 3/4 of his usual speed, we can set up a proportion to find the usual time. Let x be the usual time. We can write the proportion as (3/4)x = x + 5/2. Solving this equation, we get x = 15/2. Therefore, the usual time is 15/2.

Explanation
Let's assume the original speed of the man is x kmph. According to the given information, if he had moved 3 kmph faster, his speed would be x+3 kmph and he would have taken 40 minutes less. This can be represented as distance/speed = time, so the equation becomes d/(x+3) = t-40/60. Similarly, if he had moved 2 kmph slower, his speed would be x-2 kmph and he would have taken 40 minutes more, which can be represented as d/(x-2) = t+40/60. By solving these two equations simultaneously, we can find the value of x, which is the original speed. Once we have the speed, we can calculate the distance using the formula distance = speed * time. The distance comes out to be 40.8 km.

Explanation
To find the total distance, we need to calculate the distance covered at each speed and then add them together. Peter covers two-thirds of the distance at 4 kmph, which means he covers (2/3) * x distance at 4 kmph. He covers the remaining one-third of the distance at 5 kmph, which means he covers (1/3) * x distance at 5 kmph. Since he covers the entire distance in 1 hr 24 min, we can convert this time to hours by dividing it by 60. So, (2/3) * x / 4 + (1/3) * x / 5 = 1.4. Solving this equation, we find x = 6. Therefore, the total distance is 6.

Explanation
The two boys are walking in the same direction, so the relative speed between them is the difference of their individual speeds, which is 0.5 kmph. To find the time it takes for them to be 8.5 km apart, we divide the distance by the relative speed: 8.5 km / 0.5 kmph = 17 hrs. Therefore, it will take them 17 hours to be 8.5 km apart.

Explanation
The train and the car both cover the same distance in the same amount of time. However, the train loses 12.5 minutes while stopping at stations. This means that the total travel time for the train is longer than the total travel time for the car. Since the train can travel 50% faster than the car, it means that the car's speed is 100% of the train's speed. Therefore, the speed of the car is 120 kmph.

Explanation
Due to bad weather, the aircraft's average speed for the trip was reduced by 200 km/hr. This means that the aircraft's original average speed was 200 km/hr faster than the reduced speed. Since the distance of the flight is 600 km, we can calculate the original duration of the flight by dividing the distance by the original average speed. However, we are not given the original average speed, so we cannot calculate the exact duration of the flight. Therefore, the answer "none of these" is the most appropriate as we do not have enough information to determine the duration of the flight.

Explanation
If the man had moved 3 kmph faster, he would have taken 40 minutes less to cover the distance. This means that for every hour of travel time, the man covers 3 km less. Similarly, if the man had moved 2 kmph slower, he would have taken 40 minutes more to cover the distance. This means that for every hour of travel time, the man covers 2 km more. By comparing these two scenarios, we can deduce that the man covers 5 km less for every hour of travel time. Since the time difference is 40 minutes, which is 2/3 of an hour, the distance covered by the man is 5 km/hour * 2/3 hour = 10/3 km = 3.33 km. Therefore, the distance is approximately 40 km.

Explanation
The person's total travel time is 4 hours and 40 minutes for the return journey, which is longer than the initial journey. This indicates that the distance between hill top A and B is greater than the distance between B and A. Since the person travels downhill at a faster speed of 72 kmph, it means that the distance between A and B is longer than the distance between B and A. Therefore, the correct answer is 273, which is the only option greater than 265.

Explanation
The man traveled from the village to the post-office at a faster speed of 25 kmph and walked back at a slower speed of 4 kmph. Since the total time taken for the journey is 5 hours 48 minutes, we can convert this time to hours by dividing it by 60. So, 5 hours 48 minutes is equal to 5.8 hours.

Let's assume that the distance between the village and the post-office is 'd' km. The time taken to travel from the village to the post-office at a speed of 25 kmph is d/25 hours. The time taken to walk back from the post-office to the village at a speed of 4 kmph is d/4 hours.

According to the given information, the total time taken for the journey is 5.8 hours. So, we can write the equation as d/25 + d/4 = 5.8.

By solving this equation, we find that the distance 'd' is equal to 20 km. Therefore, the distance of the post-office from the village is 20 km.

Explanation
The ratio of their speeds can be determined by comparing the distances they travel. Since the trains cross each other at a distance of 110km from one of the stations, it means that one train has traveled 110km while the other train has traveled 200km - 110km = 90km. Therefore, the ratio of their speeds is 110km:90km, which simplifies to 11:9.