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    A man purchased 20 dozen mangoes for ₹1,000. Out of these, 40 mangoes were rotten and could not be sold. At what rate per dozen should he sell the rem
    Question

    A man purchased 20 dozen mangoes for ₹1,000. Out of these, 40 mangoes were rotten and could not be sold. At what rate per dozen should he sell the remaining mangoes to make a profit of 30%?

    A.

    ₹78

    B.

    ₹80

    C.

    ₹72

    D.

    ₹70

    Correct option is A

    Given:
    Total mangoes purchased: 20 dozen = 240 mangoes
    Cost Price (CP)= ₹1,000
    Rotten mangoes= 40
    Desired Profit= 30%
    Formula Used:
    Rate per dozen =Total SPNumber of dozen remaining \frac{\text{Total SP}}{\text{Number of dozen remaining}}
    Solution:

    Remaining mangoes=240 - 40 = 200 mangoes=20012=16.6 = \frac{200}{12} = 16.\overline{6} dozen

    SP=CP+30% of CP=1000+300=1,300\text{SP} = \text{CP} + 30\% \text{ of CP} = 1000 + 300 = ₹1,300​​
    Total Selling Price for 30% Profit:

    SP=1000+(30100×1000)=1,300\text{SP} = 1000 + \left(\frac{30}{100} \times 1000\right) = ₹1,300​​
    Convert Remaining Mangoes to Dozens:
    200 mangoes=20012=1623 dozen200 \text{ mangoes} = \frac{200}{12} = 16\frac{2}{3} \text{ dozen}

    ​Rate per dozen =13001623=1300×350=78 \frac{1300}{16\frac{2}{3}} = \frac{1300 \times 3}{50} = ₹78

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