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.

In which direction should the missing arrow point?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this be?

Until it is measured, not known. Yet how you miss it when it has gone. What is it?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

In an Art Gallary, When the clock hit 11 am, Artist hung the painting number 30. When it struck 4 pm, he hung painting number 240 and when it struck 7:30 pm, he hung painting number 315.

Can you determine, which painting number will he hang when the time is 9:20 pm?