If a shopkeeper sells sugar at ₹44.8 per kg, he is able to make a 12% profit. Due to water seepage, 1/5 of the sugar is damaged. What should now be the selling price per kg of the rest of the sugar to have a 5% profit?

Original selling price per kg = ₹44.8

Profit percentage originally = 12%

1/5 of the sugar is damaged (i.e., 20% of the sugar)

Required profit percentage = 5%

​$$\text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Profit Percentage}}{100}}$$​​

​$$\text{New Selling Price per kg} = \frac{\text{Total Cost of Undamaged Sugar} \times (1 + \frac{\text{New Profit Percentage}}{100})}{\text{Remaining Quantity of Sugar}}$$​​

​$$\text{CP} = \frac{44.8}{1 + \frac{12}{100}} = \frac{44.8}{1.12} = 40 \text{ per kg}$$​​

If 1/5 of the sugar is damaged, only 4/5 of the sugar remains. Therefore, the shopkeeper can sell only 4/5 of the total sugar, but he has incurred the cost for the entire amount.

To achieve a 5% profit on the remaining sugar, He need to sell the undamaged 4/5 of the sugar for a price that recovers the total cost plus 5% profit:

​$$\text{New SP per kg} = \frac{40 \times (1 + \frac{5}{100})}{\frac{4}{5}} \\ \ \\ = \frac{40 \times 1.05}{\frac{4}{5}}\\ \ \\= \frac{42}{\frac{4}{5}}\\ \ \\= 42 \times \frac{5}{4}\\ = 52.5 \text{ per kg}$$​​

Thus, the new selling price per kg of the undamaged sugar should be ₹52.5 to achieve a 5% profit.