A shopkeeper sells sugar at ₹44.8 per kg and makes a 12% profit. Due to water seepage, 1/5 of the sugar is damaged. What should be the new selling price per kg of the remaining sugar to achieve a 5% profit?

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Accepted Answer

Step 1: Let the cost price (CP) per kg of sugar be x.

Step 2: Given that selling price (SP) is ₹44.8 and profit is 12%.
Profit = 12% means SP = CP + 12% of CP = 1.12 × CP
So, 44.8 = 1.12 × x
=> x = 44.8 / 1.12 = ₹40 (Cost price per kg)

Step 3: Due to water seepage, 1/5 of the sugar is damaged. So, only 4/5 of the sugar is left to sell.

Step 4: The shopkeeper wants a 5% profit on the entire stock.
Total cost price for 1 kg sugar = ₹40
Total cost price for 1 kg sugar stock = ₹40

Step 5: Let the new selling price per kg of the remaining sugar be S.
Since 1/5 is damaged, the shopkeeper sells only 4/5 kg at price S per kg.
Total revenue from 4/5 kg = (4/5) × S

Step 6: To get 5% profit on the entire stock, total revenue should be 1.05 × total cost price
=> (4/5) × S = 1.05 × 40
=> S = (1.05 × 40) × (5/4) = 1.05 × 40 × 1.25 = 52.5

Therefore, the new selling price per kg should be ₹52.5 to achieve a 5% profit.

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