Quantitative Apptitude - Time & Distance Online Test 5

Explanation
The average speed of the plane around the field can be found by taking the sum of the speeds and dividing it by the number of speeds. In this case, the sum of the speeds is 200 + 400 + 600 + 800 = 2000 km/hr. Since there are four speeds, we divide the sum by 4 to find the average speed. Therefore, the average speed of the plane around the field is 2000/4 = 500 km/hr. However, none of the given options match this result. Therefore, the correct answer is not available.

Explanation
The two trains are traveling towards each other, so their combined speed is 50 kmph + 60 kmph = 110 kmph. Let's assume that the first train has traveled x km when they meet. Since the second train has traveled 120 km more than the first train, it has traveled x + 120 km. The total distance between the two trains is the sum of the distances traveled by each train, which is x + (x + 120) = 2x + 120 km. Since the combined speed of the trains is 110 kmph, the time taken to meet is (2x + 120) / 110 hours. The distance traveled by each train is equal to its speed multiplied by the time taken, so x = 50 * ((2x + 120) / 110) and solving this equation gives x = 600 km. Therefore, the total distance between the two trains is 2x + 120 = 2 * 600 + 120 = 1320 km.

Explanation
The speed of the bus without stoppages is 54 kmph, while the speed of the bus with stoppages is 45 kmph. This means that the bus is losing 9 kmph due to the time spent at stoppages. To find out how many minutes the bus stops per hour, we need to convert 9 kmph to minutes. Since 1 kmph is equal to 60 minutes, 9 kmph is equal to 9 * 60 = 540 minutes. Therefore, the bus stops for 540 minutes per hour, which is equivalent to 10 minutes.

Explanation
The man travels the first half of the journey at a speed of 21 km/hr and the second half at a speed of 24 km/hr. Since the total journey takes 10 hours, we can calculate the time taken for each half of the journey. Let's assume the total distance of the journey is 'd' km. The time taken for the first half is d/2 / 21 and the time taken for the second half is d/2 / 24. Since the total time is 10 hours, we can write the equation: d/2 / 21 + d/2 / 24 = 10. Solving this equation will give us the value of 'd', which is equal to 224 km.

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 higher than the reduced speed. Since the distance traveled is constant at 600 km, the original duration of the flight can be calculated by dividing the distance by the original average speed. Since the speed was reduced by 200 km/hr, the original average speed would be (reduced speed + 200 km/hr). The time of flight increased by 30 minutes, which is equal to 0.5 hours. Therefore, the original duration of the flight would be 600 km / (reduced speed + 200 km/hr) + 0.5 hours. Simplifying this expression, we find that the original duration of the flight is 1 hour.

Explanation
Rita covers the same distance twice, once by car and once by scooter. The time taken for each leg of the journey is inversely proportional to the speed. Since the distance is the same, the time taken for each leg is the same. Therefore, the average speed for the whole journey is the total distance divided by the total time taken, which is the sum of the speeds divided by 2. In this case, the average speed is (70 + 55) / 2 = 125 / 2 = 62.5 km/h. The closest option to this value is 61.6 km/h.

Explanation
The bus travels at a speed of 54 kmph excluding stoppages, which means that it covers 54 km in one hour. However, when including stoppages, the average speed of the bus decreases to 45 kmph. This means that the bus spends 9 kmph worth of time on stoppages, as it covers 9 km less in one hour. To find the time spent on stoppages, we can calculate the difference in time it takes to cover 9 km at a speed of 54 kmph and 45 kmph. This comes out to be 10 minutes. Therefore, the bus stops for 10 minutes per hour.

Explanation
If the train is walking at 5 of its usual speed, it means it is covering the journey at a slower pace. Since it is 10 minutes too late, we can assume that the train would have been on time if it was traveling at its usual speed. Therefore, the usual time to cover the journey is 10 minutes.

Explanation
The ratio between the speeds of the two trains is given as 7:8. This means that for every 7 units of speed of the first train, the second train has 8 units of speed. We are given that the second train runs 400 km in 4 hours. To find the speed of the first train, we can set up a proportion: 8/7 = 400/x, where x represents the speed of the first train. Solving this proportion, we find that x = 350. Therefore, the speed of the first train is 87.5.

Explanation
The man completes the first half of the journey in 10/2 = 5 hours, and the second half in the remaining 5 hours. Using the formula distance = speed × time, we can calculate the distances traveled in each half. In the first half, the distance is 21 km/hr × 5 hr = 105 km. In the second half, the distance is 24 km/hr × 5 hr = 120 km. Adding these two distances together gives us a total journey of 105 km + 120 km = 225 km. Therefore, the correct answer is 224 km.