In order to determine the change in the money supply, we must first determine the money multiplier. The money that the central bank deposits in the other banks will be multiplied as it is loaned out again and again. The amount to which its value is multiplied depends on the money multiplier which, in turn, depends on the required reserve ratio.
The formula for finding the money multiplier is:
Money multiplier = 1/required reserve ratio
In this case, since the required reserve ratio is 10%, that becomes
Money multiplier = 1/.10 = 10
Therefore, the multiplier in this case is 10.
What this means is that the money supply will go up $10 for every $1 that the central bank deposits in the private banks. Since the central bank deposited $10 million, the change in the money supply is $100 million because that is the result when we multiply the original deposits ($10 million from the sale of securities) by the multiplier (10).
So, the money supply increases by $100 million in this scenario.