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A dishonest dealer marks his goods $20\%$ above the cost price. He gives a discount of $10\%$ to the customer on the marked price and makes a profit by using a false weight of $900$ gms in place of $1$ kg while buying or selling. Find the percentage profit earned by the shopkeeper.

I do tried this problem but am not quite there,hints are welcome :-)

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The dealer doesn't actually give his customer a discount. He charges 90% of the price for 90% of the product. Thus he still makes a 20% profit over the supplier price. Let $C$ be the supplier price for 1 kg of product. The dealer then gets 1.1kg for the price $C$ or 1kg for $10\over{11}$$C$. He sells this 1kg for $1.2C$. The profit margin is $1.2C$-$10\over{11}$$C$ divided by the dealer price, $10\over{11}$$C$, which I calculate to be 32%.

Here I have assumed the "cost price" is the supplier price, $C$. If you assume the cost price is what the dishonest dealer actually pays his supplier, you will get a different answer still.

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The dealer uses false weight in both buying and selling,so he buys $1100$ gm and sells $900$ gms. – Quixotic Jan 2 '11 at 11:16

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