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

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Find out the missing number in the picture attached:

We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube?

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

What's a single-digit number with no value?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

John went to buy some expensive, foreign chocolates. He only had Rs 100 with him. When he reached the shop, he got out and know that on those chocolates, there was a 15% import duty and 5% VAT.

How much worth chocolate should he buy so that he can accommodate it in Rs 100?