Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

A brand new Mobile Phone was on sale at 20% as a promotional offer. By what per cent must the Mobile price be increased to sell it at the original price again?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

A Shopkeeper collects 71 rupees in the form of 20 paisa and 25 paisa.
He collects a total of 324 coins.

Can you tell me how many number of 20-paisa and 25-paisa he got?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

The Puzzle: Here is a famous prize problem that Sam Loyd issued in 1882, offering $1000 as a prize for the best answer showing how to arrange the seven figures and the eight 'dots' .4.5.6.7.8.9.0. which would add up to 82

John can place six large boxes or nine small boxes into a carton.

Can you find out in how many cartons can he place sixty-six boxes in total?

A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result.

Can you find how bias is the floor in this case?