What is the profit percentage of a dishonest cloth merchant who uses a scale which measures $$16\frac{2}{3}$$% less than what is marked on it, and also sells at a price 10% higher than the cost price?

Let's assume that the cost price of 1 cm of cloth is Rs. 10.

He sells at a price 10% higher than the cost price

Selling price of 1 cm = 10 of (100+10)%

= 10 of 110%

= 11

Let's assume that he marked 6 cm of cloth to sell. But as per the question, he did $$16\frac{2}{3}$$% cheating in the measurement.

Actual quantity of cloth sold = 6 of $$(100-16\frac{2}{3})$$%

= $$6\ of\ (100-\frac{50}{3})\%$$

= $$6\ of\ (\frac{300-50}{3})\%$$

= $$6\times\frac{250}{300}$$

= 5 cm

So the cost price of 5cm cloth = $$5\times10$$

= 50    Eq.(i)

Selling price of 6cm cloth (in actual it was 5cm because of cheating) = $$6\times11$$

= 66    Eq.(ii)

Profit percentage = $$\frac{selling\ price - cost\ price}{cost\ price}\times100$$

= $$\frac{Eq.(ii)-Eq.(i)}{Eq.(i)}\times100$$

= $$\frac{66-50}{50}\times100$$

= $$\frac{16}{50}\times100$$

= 32%