What does an Island and the letter T have in common?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

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?

Jack have ten pairs of black socks, eight pairs of white socks and seven pairs of green socks. Everything is mixed in a draw. As there is no light he were not able to identify the colour of the socks. How many of the socks did he want to take to match one pair

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

John was piloting a plane behind a car but was never able to overtake it. Why?

A pet show was happening in my locality. I went down along with my kids. In that show, I noticed that all except two of the entries were cats. All except two were dogs and all except two were Monkeys.

Can you find out how many of each animals were present in that pet show?