High School

A fruit seller bought 20 kg of oranges at Rs 72 per kg. He sold 20% of them at Rs 85 per kg. Due to inadequate storage, 20% of the total oranges got rotten. At what approximate price should he sell the remaining oranges to earn an overall profit of 12%?

(a) Rs 92 per kg
(b) Rs 106 per kg
(c) Rs 98 per kg
(d) Rs 112 per kg

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.

  1. 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]

  2. 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]

  3. 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]

  4. 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]

  5. 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]

  6. 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]

  7. 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