Question : A dishonest shopkeeper pretends to sell his goods at a cost price but uses false weights and gains 10%. How much false weight he is using instead of 1 kg weight?
Option 1: 909.09 g
Option 2: 900 g
Option 3: 920.30 g
Option 4: 911.12 g
Correct Answer: 909.09 g
Solution :
Let the false weight as $x$ kg.
The shopkeeper is gaining 10% by using this false weight, which means that when he claims to sell 1 kg of goods, he is only giving away $x$ kg.
The cost price of $x$ kg of goods is being sold as the cost price of 1 kg of goods, which is a 10% gain.
Let the cost price of 1 kg be Re. 1.
$\frac{\text{1} }{{\text{Cost price of } x \text{ kg}}} = 1 + \frac{{10}}{{100}}$
⇒ $x = \frac{{1}}{{1.1}} = 0.90909 \text{ kg}= 909.09 \text{ g}$
Hence, the correct answer is 909.09 g
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