There is a profit of 10% when an item is sold at $$\frac{5}{6}$$ of its actual selling price. What will be the profit percentage on the cost price when the item is sold at its actual selling price?

There is a profit of 10% when an item is sold at $$\frac{5}{6}$$ of its actual selling price.

Let's assume the actual selling price is '6y'.

item is sold at = $$6y\times\frac{5}{6}$$ = 5y

cost price of item = $$\frac{5y}{\left(100+10\right)}\times\ 100$$

= $$\frac{5y}{110}\times\ 100$$

= $$\frac{50y}{11}$$
Profit percentage on the cost price when the item is sold at its actual selling price = $$\frac{6y-\frac{50y}{11}}{\frac{50y}{11}}\times100$$

= $$\frac{\frac{66y-50y}{11}}{\frac{50y}{11}}\times100$$

= $$\frac{16y}{50y}\times100$$

= 32%