money supply, interest rates and inflation holding, interest, someone, decrease, getting

TheMBAGlover

Could someone explain the linkage between money supply interest rates and inflation? I keep getting confused.

Take this Q for example:

Households hold more real money than they desire which is least likely to happen?

1)The interest rate is higher than its equilibrium rate in the market for real money balances
2)The central bank must sell securities to absorb the excess money supply and establish equilibrium.
3)The opportunity cost of holding money balances will decrease.

The answer is 2), but the comments along with the answer baffled me!
"If households’ real money balances are larger than they desire, the interest rate (opportunity cost of holding money balances) is higher than its equilibrium rate. Households will use their undesired excess cash to buy securities, bidding up securities prices and reducing the interest rate toward equilibrium. This market process does not require any action by the central bank."

If households buy securities, i.e. Treasury sells and so reduce money supply - does decrease of money supply not lead to a reduction in inflation and therefore an increase in interest rate??