A shopkeeper purchased groundnuts at ₹64/kg and sells at ₹80/kg. While selling, he uses faulty weights and gives 800 gm instead of 1 kg. Find his actual profit percentage.

Let's consider the cost price of 1000 gm (1 kg) of groundnuts is ₹64.Therefore, the cost price of 800 gm given to the customer is:
$$\text{CP of 800 gm}=\frac{64}{1000}\times 800=₹51.20$$
The selling price charged to the customer for this quantity (under the pretense of 1 kg) is ₹80.
$$\text{SP}=₹80$$
Actual Profit = $\text{SP}-\text{CP}=80-51.20=₹28.80$ Actual Profit Percentage:
$$\text{Profit }\%=\left(\frac{\text{Actual Profit}}{\text{Actual CP}}\right)\times 100$$
$$\text{Profit }\%=\left(\frac{28.80}{51.20}\right)\times 100=\frac{288}{512}\times 100=\frac{9}{16}\times 100=56.25\%$$