Quantitative Apptitude - Time & Distance Online Test 8

Explanation
The average speed is calculated by dividing the total distance traveled by the total time taken. In this case, the person walks at 5kmph for 6 hours, covering a distance of 5kmph * 6hr = 30km. Then, the person walks at 4kmph for 12 hours, covering a distance of 4kmph * 12hr = 48km. The total distance traveled is 30km + 48km = 78km. The total time taken is 6hr + 12hr = 18hr. Therefore, the average speed is 78km / 18hr = 13/3 kmph.

Explanation
The man and woman are traveling towards each other, so their combined speed is 5 + 4 = 9 miles per hour. To find the distance the woman will have traveled when they meet, we can use the formula distance = speed × time. Since their combined speed is 9 miles per hour, and they are 81 miles apart, the time it takes for them to meet is 81 / 9 = 9 hours. Therefore, the woman will have traveled 4 miles per hour × 9 hours = 36 miles when they meet.

Explanation
Robert needs to reach point A at 1 P.M., which is one hour earlier than his original plan of reaching at 2 P.M. If he travels at 10 kmph, he will take 2 hours to reach point A, and if he travels at 15 kmph, he will take 1.5 hours to reach point A. Therefore, to reach point A at 1 P.M., he needs to travel at a speed that will allow him to cover the distance in 1 hour. The only option that satisfies this condition is 12 kmph, as it will take him exactly 1 hour to reach point A at this speed.

Explanation
The car is traveling at 5/7 of its actual speed, and it covers 42 km in 1 hr 40 min 48 sec. To find the actual speed, we need to convert the time to hours. Since there are 60 minutes in an hour and 60 seconds in a minute, 1 hr 40 min 48 sec is equal to (1 + 40/60 + 48/3600) hours. Simplifying this, we get 1.68 hours.

Now, we can use the formula: Speed = Distance / Time. Plugging in the values, we have: Actual Speed = 42 km / 1.68 hours = 25 kmph.

Therefore, the correct answer is 35 kmph.

Explanation
Let the actual velocity of the car be V km/hr and the distance between A and B be D km.

In the first scenario, when the car travels 30 km with 4/5th of its actual velocity, the time taken can be calculated as 30 / (4/5)V = 37.5/V hours. This is 45 minutes (or 0.75 hours) more than the actual time.

In the second scenario, when the car travels 45 km with its actual velocity, the time taken is 45 / V hours. This is 36 minutes (or 0.6 hours) more than the actual time.

From the given information, we can set up the following equations:
37.5/V = (actual time) + 0.75
45/V = (actual time) + 0.6

Solving these equations, we can find V = 75 km/hr.

Substituting this value of V in either of the equations, we can find the actual time taken to travel the distance D.

Since the car reaches B in both scenarios, the actual time taken in both cases should be the same.

Therefore, we can equate the two equations:
37.5/75 = 45/D

Solving for D, we get D = 130 km.

Explanation
Let's assume Sameer's speed is S kmph and Abhay's speed is A kmph. We are given that Abhay takes 2 hours more than Sameer to cover a distance of 30 km, so we can write the equation: 30/A = 30/S + 2.
We are also given that if Abhay doubles his speed, he would take 1 hour less than Sameer, so we can write the equation: 30/2A = 30/S - 1.
Simplifying both equations, we get: 2S - A = 15 and 4S - 2A = 30.
Solving these equations simultaneously, we find that S = 10 kmph and A = 5 kmph. Therefore, Abhay's speed is 5 kmph.

Explanation
Train B's wheels will wear first because it is traveling in the opposite direction of the Earth's spin. This means that it will experience more friction and resistance from the Earth's rotation, causing its wheels to wear out faster compared to Train A.

Explanation
The farmer travelled a total distance of 61 km in 9 hours. Let's assume he travelled x km on foot and (61-x) km on a bicycle. The time taken to travel x km on foot would be x/4 hours, and the time taken to travel (61-x) km on a bicycle would be (61-x)/9 hours. Since the total time taken is 9 hours, we can write the equation x/4 + (61-x)/9 = 9. Solving this equation, we find x = 16. Therefore, the farmer travelled 16 km on foot.

Explanation
If walking both ways takes 55 minutes and walking one way and riding back takes 37 minutes in total, we can subtract the time it takes to walk one way from the total time to find the time it takes to ride back. So, 37 minutes - 55 minutes = -18 minutes. However, since time cannot be negative, we can assume that the negative sign was a typo and it should be positive. Therefore, it would take 18 minutes to ride back. Since we need to consider both ways, we can double this time to get the total time to ride both ways, which is 18 minutes x 2 = 36 minutes. However, since none of the given options match this answer, the correct answer is not available.