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Answer :
To determine the price at which the remaining oranges should be sold to achieve an overall profit of 12%, let's work through the problem step-by-step.
Cost of Oranges:
The fruit seller bought 20 kg of oranges at Rs 72 per kg.
[tex]\text{Total Cost} = 20 \times 72 = \text{Rs } 1440[/tex]
Oranges Sold and Price:
The seller sold 20% of these 20 kg of oranges at Rs 85 per kg.
[tex]\text{Weight Sold} = 20\% \times 20 = 4 \text{ kg}[/tex]
[tex]\text{Revenue from Sold Oranges} = 4 \times 85 = \text{Rs } 340[/tex]Oranges Rotten:
Due to inadequate storage, another 20% of the total oranges became rotten and cannot be sold.
[tex]\text{Weight of Rotten Oranges} = 20\% \times 20 = 4 \text{ kg}[/tex]
Oranges Remaining for Sale:
Initially there were 20 kg, 4 kg were sold, and 4 kg went rotten,
so the remaining oranges are:[tex]\text{Remaining Oranges} = 20 - (4 + 4) = 12 \text{ kg}[/tex]
Target Revenue for 12% Profit:
To achieve an overall profit of 12%, the fruit seller's revenue should be:
[tex]\text{Target Revenue} = 1440 \times (1 + 0.12) = \text{Rs } 1612.8[/tex]
Revenue Required from Remaining Oranges:
Subtract the revenue already earned from sold oranges to find out how much more revenue is needed:
[tex]\text{Revenue Needed} = 1612.8 - 340 = \text{Rs } 1272.8[/tex]
Price per KG for Remaining Oranges:
Divide the required revenue by the weight of the remaining oranges to find the required selling price per kg:
[tex]\text{Price per kg} = \frac{1272.8}{12} \approx \text{Rs } 106.07[/tex]
Therefore, the approximate price per kg at which he should sell the remaining oranges is Rs 106.
The correct option is: (b) Rs 106 per kg
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