If 21x = 79x, what is the value of x?

Can you think of any three-dimensional shape that comprises of exactly two surfaces?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A man always keeps a spare tyre in his car. To make full use of all the five tyres, he changes the tyres in a manner that for a distance of 1, 00,000 km, each of them runs the same distance.

Can you calculate the distance travelled by each tyre on that journey?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?