Puzzling question

A number divided by 713 gives 115 as remainder. IF the same number is divided by 31, what will be the remainder?
Question asked by: Chanakya69

Asked on: 09 Nov 2008

Let Y be the quotient.Now, as the no. was divided by 713, Y is the quotient and 115 is the remainder, so the number should be 713Y+115.

Now if we divide 713 by 31 we get 23 as quotient. So we can write 713*Y+115 as 31*23*Y+115. We can also write 115 as 31*3+22.
Now we can write
(31*23+31*3+22)/31
=> [(31*23*Y)/31]+[(31*3+22)/31]
=> [(31*23*Y)/31]+[(31*3+22)/31]
=> (23*Y)+(3+22)

The answer will be 22.
By: Chanakya69
Replied at: 12 Nov 2008
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