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    A shopkeeper buys three varieties of sugar at Rs 99, Rs 120 and Rs 144 per kg respectively and mixes them in the ratio 9 : 2 : 1. In order to earn a&n
    Question

    A shopkeeper buys three varieties of sugar at Rs 99, Rs 120 and Rs 144 per kg respectively and mixes them in the ratio 9 : 2 : 1. In order to earn a y% profit after giving a discount equal to a sixth of the marked price, the marked price per kg of the blended sugar is fixed at Rs 178.50. What is the value of y?

    A.

    35

    B.

    40

    C.

    45

    D.

    36

    Correct option is B

    Given:

    Prices of three varieties of sugar:

    First variety: ₹99 per kg

    Second variety: ₹120 per kg

    Third variety: ₹144 per kg

    The mixing ratio is 9 : 2 : 1.

    Marked price per kg of the blended sugar = ₹178.50.

    Discount on the marked price = 16\frac{1}{6} ​of the marked price.

    The shopkeeper wants to earn a profit of y%.

    Formula Used:

    SP = Marked Price - Discount

    Discount =  16×Marked Price\frac{1}{6} \times \text{Marked Price}​​

    SP = Marked Price - 16×Marked Price=56×Marked Price\frac{1}{6} \times \text{Marked Price} = \frac{5}{6} \times \text{Marked Price}​​

    y = ProfitCost Price×100\frac{\text{Profit}}{\text{Cost Price}} \times 100​​

    Solution:

                         A        :        B         :        C

    Price →      99               120              144

    Quantity → 9                  2                  1    = 12

    CP = (9×99)+(2×120)+(1×144)9+2+1\frac{(9 \times 99) + (2 \times 120) + (1 \times 144)}{9 + 2 + 1}​​

    CP = 891+240+14412=127512=106.25\frac{891 + 240 + 144}{12} = \frac{1275}{12} = ₹106.25​​

    SP = 56×178.50=148.75\frac{5}{6} \times 178.50 = ₹148.75​​

    Profit = 148.75 - 106.25 = ₹42.50

    y = 42.50106.25×100=40%\frac{42.50}{106.25} \times 100 = 40\%​​

    Thus, the correct option is (b)  40


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