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

While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:

'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are to go!

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

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

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

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

You need to arrange three 7 and mathematical symbols to form number 1?

How do you go from 98 to 720 using just one letter?

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?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

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