A dealer bought an item at a discount of 10% on its original price. He sold it for an amount 35% more than the original price. What percentage of profit did he get?

Let's assume the original price is 100y.

A dealer bought an item at a discount of 10% on its original price.

Actual cost price after discount = 100y of (100-10)%

= 100y of 90%

= $$100y\times\frac{90}{100}$$

= 90y    Eq.(i)

He sold it for an amount 35% more than the original price. 

Selling price = (100+35)% of original price

= 135% of original price

= 135% of 100y

= $$\frac{135}{100}\times100y$$

= 135y    Eq.(ii)

Percentage of profit = $$\frac{\left(Eq.(ii)-Eq.(i)\right)}{Eq.(i)}\times100$$

= $$\frac{\left(135y-90y\right)}{90y}\times100$$

= $$\frac{45y}{90y}\times100$$

= $$\frac{1}{2}\times100$$

= 50%