A shopkeeper sold his goods at the cost price. By using false weights, he gained \(11\frac{1}{9}\%\). What weight did he use for 1 kg?
900 gm
Let the shopkeeper use a weight of \(w\) grams in place of 1000 g while charging for 1 kg. Since the goods are sold at cost price, the entire gain comes from the false weight: \(\text{Gain \%} = \frac{1000-w}{w}\times 100\). Given the gain is \(11\frac{1}{9}\% = \frac{100}{9}\%\), so \(\frac{1000-w}{w}=\frac{1}{9}\), giving \(9000-9w=w \Rightarrow w=900\). So he used a 900 g weight for 1 kg.
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