# A dishonest shopkeeper has two false balances. One balance wieghs 10% more while buying the goods and other weighs 10% less while selling the goods then what is his gain percent just by weighing?

Sep 17, 2017

Shopkeepers gain just by weighing is 22.22%

#### Explanation:

Assume that theshopkeeper bought $x$ units of goods i.e. actual weight of goods.

As the balance used to buy goods weighs 10% more, he actually bought $x \times \frac{110}{100} = 1.1 x$ weight units i.e. although the shopkeeper paid for $x$ units, he actully bought $1.1 x$ units by weight.

Now he has $1.1 x$ units of goods, but for selling he uses another balance, which actually measures 10% less i.e. $1 - 0.10 = 0.9$ units for each unit weight of goods sold.

So while selling $1.1 x$ becomes $\frac{1.1 x}{0.90} = 1.2222 \ldots$ units.

Hence, shopkeepers gain just by weighing is 22.22%