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    Question

    A’, β€˜B’ and β€˜C’ started a business by

    investing Rs. 8,000, Rs. 9,500, and Rs. 7,500, respectively such that β€˜B’ invested for 2 months more than β€˜C’ and 6 months less than β€˜A’. If the ratio of profit share of β€˜A’ to the average of profit share of β€˜B β€˜and β€˜C’ together is 50:27, respectively, then find the time for which β€˜B’ invested his sum.
    A 12 Correct Answer Incorrect Answer
    B 8 Correct Answer Incorrect Answer
    C 10 Correct Answer Incorrect Answer
    D 6 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    According to the question: Let the number of months for which β€˜C’ invested his sum = β€˜x’ months Then, number of months for which β€˜B’ invested his sum = (x + 2) months Number of months for which β€˜A’ invested his sum = x + 2 + 6 = (x + 8) months So, the ratio of profit shares of β€˜A’, β€˜B’, and β€˜C’, respectively: = {8000 Γ— (x + 8)}:{9500 Γ— (x + 2)}:{7500 Γ— x} = (8000x + 64000):(9500x + 19000):(7500x) Average of profit share of β€˜B’ and β€˜C’: = (9500x + 7500x + 19000) Γ· 2 = Rs. (8500x + 9500) According to the question: (8000x + 64000):(8500x + 9500) = 50:27 Or, 50(8500x + 9500) = 27(8000x + 64000) Or, 425000x + 475000 = 216000x + 1728000 Or, 209000x = 1253000 So, x = 6.00 So, the number of months for which β€˜B’ invested = x + 2 = 6 + 2 = 8 months

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