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    Find the ratio at which rice at Rs.15.20 per kg is mixed with rice at Rs.18.10 per kg to get a mixture worth Rs.16.30 per kg.
    Question

    Find the ratio at which rice at Rs.15.20 per kg is mixed with rice at Rs.18.10 per kg to get a mixture worth Rs.16.30 per kg.

    A.

    15:13

    B.

    13:15

    C.

    11:18

    D.

    18:11

    Correct option is D

    Given:
    ​Price of first type of rice = Rs. 15.20/kg
    Price of second type of rice = Rs. 18.10/kg
    Price of the mixture = Rs. 16.30/kg

    Formula Used:
    Price per kg=Total CostTotal Weight\text{Price per kg} = \frac{\text{Total Cost}}{\text{Total Weight}}

    Solution:
    ​Let's assume we mix x kg of rice at Rs. 15.20/kg with y kg of rice at Rs. 18.10/kg.
    Cost of x kg of rice = 15.20x
    Cost of y kg of rice = 18.10y

    Total cost = 15.20x + 18.10y
    Total weight = x + y

    Price per kg=Total CostTotal Weight\text{Price per kg} = \frac{\text{Total Cost}}{\text{Total Weight}}
    ​​
    16.30=15.20x+18.10yx+y16.30 = \frac{15.20x + 18.10y}{x + y}
    ​​16.30x+16.30y=15.20x+18.10y16.30x + 16.30y = 15.20x + 18.10y​​
    1.10x=1.80y1.10x = 1.80y​​
    xy=1.801.10xy=1811\frac{x}{y} = \frac{1.80}{1.10} \\\frac{x}{y} = \frac{18}{11}

    ​​Therefore, the ratio of the two types of rice is 18:11.

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