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    A person buys some oranges at the rate of 3 for 1 rupee and some more oranges at the rate of 2 for 1 rupee. He sells all the oranges at a profit of 20
    Question

    A person buys some oranges at the rate of 3 for 1 rupee and some more oranges at the rate of 2 for 1 rupee. He sells all the oranges at a profit of 20%. What is the selling price of 1 dozen oranges?

    A.

    ₹7

    B.

    ₹4

    C.

    ₹5

    D.

    ₹6

    Correct option is D

    Formula Used:

    S.P=C.P(1±P or L100)S.P = C.P \left(1 \pm \frac{P \text{ or } L}{100}\right)​​

    Solution:

    Let the man buy 1 dozen oranges in both cases

    When a man buys 3 oranges for Rs. 1

    Price of one orange = 13\frac 13​​

    Price of 1 dozen oranges = 13\frac 13​ × 12 = Rs. 4

    Similarly, when a man buys 2 oranges for Rs. 1

    Price of 1 dozen oranges = 12\frac12​ × 12 = Rs. 6

    Cost price for 2 dozens = 4 + 6 = Rs. 10 

    Cost price for 1 dozen =102 \frac {10}2​ = Rs. 5

    We know that, 

    S.P=C.P(1+P100)S.P=5(1+20100)=Rs. 6S.P = C.P \left(1 + \frac{P}{100}\right) \\S.P = 5 \left(1 + \frac{20}{100}\right) = \text{Rs. } 6​​

    ∴ The selling price will be Rs. 6

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