Final answer:
To calculate the shopkeeper's profit percentage when selling rice at market price, we must deduct the discounted cost price from the selling price and divide by the cost price per kg, then multiply by 100. The shopkeeper benefits from both a 10% discount and additional free rice for buying in bulk, which contributes to a higher profit margin when selling the rice at its market value.
Step-by-step explanation:
To determine the shopkeeper's profit percentage when selling rice, we need to calculate the cost price, the selling price, and then use these values to find the profit margin. Initially, the shopkeeper bought 80 kg of rice at a discount of 10%, which effectively reduces the cost price of the rice. On top of that, for every 20 kg of rice purchased, he received an additional 1 kg of rice for free, which means he received 4 kg of rice free in total (1 kg for each 20 kg, and he bought 80 kg).
Let's denote the original price per kg of rice as 'P'. The discount on this price is 10%, so the shopkeeper pays 90% of P for each kg, which can be represented as 0.9P. The cost price for 80 kg of rice is therefore 80 × 0.9P. However, since he received 4 kg of rice for free, the effective quantity of rice that the cost price will be divided by is 84 kg. Thus, the cost price per kg of rice is (80 × 0.9P) / 84.
Assuming that the market price is 'P' without any discount, and since the shopkeeper sells the rice at the market price, his selling price per kg is P. The profit per kg of rice is the selling price minus the cost price, which can be expressed as P - (80 × 0.9P) / 84. To find the profit percentage, we divide the profit per kg by the cost price per kg and multiply by 100.
Without specific numerical values for 'P', we cannot calculate the actual profit percentage. However, in a real-world scenario, the shopkeeper would insert the actual cost values to determine his profit percentage and decide on his selling strategy accordingly.