Math Riddles

John and Jacob are planning on a vacation. John says, "It will be better if we take the train to the hotel. We will reach faster."
To this, Jacob says, "No. You are wrong. The train stops halfway to the hotel and then we will have to walk the rest of the way. We should take the bikes to the hotel directly."
John says, "You are wrong."

Now, John takes the train while Jacob takes the bike. The train travels at four times the speed of the bike. The bike travels at twice the speed of walking.

Who do you think will reach the hotel first?

Cristina learnt how to ride a horse recently. Just to test her skills, she rode the horse from her home to a mine which she covered in three minutes and returned home from the same path only this time she took four minutes. The reason was that while riding away from home, she was supported by the wind however while riding back, she was riding against the wind.

How fast do you think she could have ridden a mile if there was no wind?

A lily pad doubles in size every day. If on the 60th day, the pond is exactly filled with the lily pad, on what day is the pond exactly half covered?

You are playing a probability game with your friend using a fair coin. Both of you decide on a particular sequence that you have to achieve.

Let us suppose you chose the sequence to be: H T H
Your friend chose the sequence to be: H T T

Now you keep tossing coins until you get the sequence and the same is done by your friend. You keep doing that till you achieve your predefined sequence and keep writing the result on paper. At the end of the game the player whose average number of tosses will be lowest, he will win.

The results of the game 1 toss:
You: H T T H T H
Your score: 6
Your friend: H T H H H T H H T T
Your friends' score: 10

The results of the game 2 toss:
You: T T H T T H H T H
Your score: 9
Your friend: T T H H T H T T
Your friends' score: 8

The results of the game 3 toss:
You: T T H H T H
Your score: 6
Your friend: H H T H T T
Your friends' score: 6

Now after 3 games, your average score is 7 and your friend's average score is 8. Now assume that you keep playing the game and play many times. What will be the possible outcome of the following?

a) You win
b) Your friend win
c) Tie

John is now two fifth of his older brother's age and two years from now he will be half of his older brother's age.
Two years ago, John was only one-fourth the age of his older brother age at that time.

How old is John now?

In a certain country ½ of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10?

Find the value of "a" by solving the maths equation in the picture below:

There is one four-digit whole number n, such that the last four digits of n2 are the original number n

In a school, 280 students studied chemistry, 254 students studied physics and 280 students studied biology.

97 students studied chemistry as well as physics, 138 students studied physics as well as biology and 152 students studied chemistry as well as biology.

73 students studied all the three branches.

Can you find out the total number of students?