A retailer bought 50 kg of Arhar Dal at a discount of 20%. Another 2 kg of Arhar dal was offered to him for free by the wholesaler on the purchase of 50 kg of the Arhar dal. If the retailer sells the entire quantity of the Arhar dal at the marked price to a customer, what is the profit percentage gained by the retailer?

Let's assume the marked price of Arhar Dal for each kg is '10y'.

A retailer bought 50 kg of Arhar Dal at a discount of 20%.

Total cost price of 50 kg of Arhar Dal = 50 $$\times$$ 10y of (100-20)%

= 50 $$\times$$ 10y of 80%

= 50 $$\times$$ 8y

= 400y    Eq.(i)

Another 2 kg of Arhar dal was offered to him for free by the wholesaler on the purchase of 50 kg of the Arhar dal. If the retailer sells the entire quantity of the Arhar dal at the marked price to a customer.

Total selling price of 52 kg of Arhar Dal = $$52\times$$10y = 520y    Eq.(ii)

profit percentage gained by the retailer = $$\frac{\left(Eq.(ii)-Eq.(i)\right)}{Eq.(i)}\times100$$

= $$\frac{\left(520y-400y\right)}{400y}\times100$$

= $$\frac{120y}{400y}\times100$$

= $$3\times10$$
= 30%