__Question 1__
A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

The correct choice is (A) and the correct answer is

**240 meters**.

**Explanatory Answer**

When the train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.

However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.

The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover = length of the platform.

Therefore, length of the platform = speed of train * extra time taken to cross the platform

Length of platform = 72 kmph * 12 seconds

Converting 72 kmph into m/sec, we get 72 kmph = 5/18 * 72 = 20 m/sec

Therefore, length of the platform = 20 * 12 = 240 meters.

However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.

The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover = length of the platform.

Therefore, length of the platform = speed of train * extra time taken to cross the platform

Length of platform = 72 kmph * 12 seconds

Converting 72 kmph into m/sec, we get 72 kmph = 5/18 * 72 = 20 m/sec

Therefore, length of the platform = 20 * 12 = 240 meters.

__Question 2__
A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?

- 1777 meters
- 1822 meters
- 400 meters
- 1111 meters
- None of these

The correct choice is (C) and the correct answer is

**400 meters**.**Explanatory Answer**

When a train overtakes another object such as a motorbike, whose length is negligible compared to the length of the train, then the distance traveled by the train while overtaking the motorbike is the same as the length of the train.

The length of the train = distance traveled by the train while overtaking the motorbike

= relative speed between the train and the motorbike * time taken

In this case, as both the objects i.e., the train and the motorbike are moving in the same direction, the relative speed between them = difference between their respective speeds = 100 - 64 = 36 kmph.

Distance traveled by the train while overtaking the motorbike = 36 kmph * 40 seconds.

The final answer is given in meters and the speed is given in kmph and the time in seconds.

So let us convert the given speed from kmph to m/sec.

1 kmph = (5/18) m/sec

Therefore, 36 kmph = 36 * (5 /18) = 10 m/sec.

Relative speed = 10 m/sec. Time taken = 40 seconds.

Therefore, distance traveled = 10 * 40 = 400 meters.

The length of the train = distance traveled by the train while overtaking the motorbike

= relative speed between the train and the motorbike * time taken

In this case, as both the objects i.e., the train and the motorbike are moving in the same direction, the relative speed between them = difference between their respective speeds = 100 - 64 = 36 kmph.

Distance traveled by the train while overtaking the motorbike = 36 kmph * 40 seconds.

The final answer is given in meters and the speed is given in kmph and the time in seconds.

So let us convert the given speed from kmph to m/sec.

1 kmph = (5/18) m/sec

Therefore, 36 kmph = 36 * (5 /18) = 10 m/sec.

Relative speed = 10 m/sec. Time taken = 40 seconds.

Therefore, distance traveled = 10 * 40 = 400 meters.

__Question 3__
Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?

- 42 mph
- 36 mph
- 37.5 mph
- 42.5 mph
- 48 mph

The correct choice is (C) and the correct answer is

**37.5 mph**.**Explanatory Answer**

Average speed = total distance/total time

Total distance traveled by Jim = Distance covered in the first 3 hours + Distance covered in the next 5 hours.

Distance covered in the first 3 hours = 3 * 60 = 180 miles

Distance covered in the next 5 hours = 5 * 24 = 120 miles

Therefore, total distance traveled = 180 + 120 = 300 miles.

Total time taken = 3 + 5 = 8 hours.

Average speed = 300/8= 37.5 mph.

Total distance traveled by Jim = Distance covered in the first 3 hours + Distance covered in the next 5 hours.

Distance covered in the first 3 hours = 3 * 60 = 180 miles

Distance covered in the next 5 hours = 5 * 24 = 120 miles

Therefore, total distance traveled = 180 + 120 = 300 miles.

Total time taken = 3 + 5 = 8 hours.

Average speed = 300/8= 37.5 mph.

__Question 4__
A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?

- 10 meters
- 25 meters
- 45 meters
- 15 meters
- 35 meters

The correct choice is (E) and the correct answer is

**35 meters**.**Explanatory Answer**

A runs 25% as fast as B.

That is, if B runs 100m in a given time, then A will run 125m in the same time

In other words, if A runs 5m in a given time, then B will run 4m in the same time.

Therefore, if the length of a race is 5m, then A can give B a start of 1m so that they finish the race in a dead heat.

Start : length of race :: 1 : 5

In this question, we know that the start is 7m.

Hence, the length of the race will be 7 * 5 = 35m.

That is, if B runs 100m in a given time, then A will run 125m in the same time

In other words, if A runs 5m in a given time, then B will run 4m in the same time.

Therefore, if the length of a race is 5m, then A can give B a start of 1m so that they finish the race in a dead heat.

Start : length of race :: 1 : 5

In this question, we know that the start is 7m.

Hence, the length of the race will be 7 * 5 = 35m.

__Question 5__
Jane covered a distance of 340 miles between city A and city taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?

- 2 hours 30 minutes
- 3 hours
- 2 hours
- 1 hour 45 minutes
- None of these

The correct choice is (B) and the correct answer is

**3 hours**.**Explanatory Answer**

Let 'x' hours be the time for which Jane traveled at 60 miles per hour.

As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.

Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles

Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x miles

Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.

Therefore, total distance = 60x + 400 - 80x.

But, we know that the total distance = 340 miles.

Therefore, 340 = 60x + 400 - 80x

=> 20x = 60 or x = 3 hours.

As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.

Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles

Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x miles

Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.

Therefore, total distance = 60x + 400 - 80x.

But, we know that the total distance = 340 miles.

Therefore, 340 = 60x + 400 - 80x

=> 20x = 60 or x = 3 hours.

__Question 6__
Steve traveled the first 2 hours of his journey at 40 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?

- 60 mph
- 56.67 mph
- 53.33 mph
- 64 mph
- 66.67 mph

The correct choice is (D) and the correct answer is

**64 mph**.**Explanatory Answer**

Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.

Distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles

Distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles

Therefore, total distance covered = 80 + 240 = 320 miles

Total time taken = 2 + 3 = 5 hours.

Hence, average speed = 320/5= 64 miles per hour.

**Note:**If Steve had traveled equal amount of time at 40 mph and 80 mph, then his average speed will be the arithmetic mean (or simple average) of the two speeds.