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.

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

If we add four times the age of John four years from now to five times his age five years from now we get ten times his current age.

How old will John be two years from now?

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

Can you make numbers like 24, using numbers 3,3,7 & 7 with any arithmetic operator?

Can you find out the remainder when 3^300 is divided by 5?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

Replace the (?) with the correct mathematical signs to make the expression equal to 59.

18 ? 12 ? 4 ? 5 = 59

Can you find out which number multiplied by itself will give the output as 12345678987654321?

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