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    Question

    After 2 years, the ratio between the compound interest

    obtained from scheme A and B is 99:115 respectively. The total initial investment of both of the schemes (A and B) together is Rs. 70500. The compound interest obtained from scheme C after 2 years at the rate of 25% per annum is Rs. 25312.5. The initial investment of scheme A is 10% less than the initial investment of scheme C. If the rate of interest in scheme B is 30%, then find out the rate of interest in scheme A. In each of the schemes interest is compounded annually.
    A 25% Correct Answer Incorrect Answer
    B 15% Correct Answer Incorrect Answer
    C 35% Correct Answer Incorrect Answer
    D 20% Correct Answer Incorrect Answer
    E 40% Correct Answer Incorrect Answer

    Solution

    The compound interest obtained from scheme C after 2 years at the rate of 25% per annum is Rs. 25312.5.

    Let’s assume the initial investment of scheme C is ‘c’.

    25312.5 = c of 125% of 125% - c

    25312.5 = 1.5625c - c

    25312.5 = 0.5625c

    c = 45000

    The initial investment of scheme A is 10% less than the initial investment of scheme C.

    initial investment of scheme A = (100-10)% of 45000

    = 90% of 45000

    = 40500

    The total initial investment of both of the schemes (A and B) together is Rs. 70500.

    initial investment of scheme B = 70500-40500 = 30000

    After 2 years, the ratio between the compound interest obtained from scheme A and B is 99:115 respectively. If the rate of interest in scheme B is 30%.

    interest from scheme B after 2 years = 30000 of 130% of 130% - 30000

    = 50700 - 30000

    = 20700

    interest from scheme A after 2 years = (20700/115)x99 = 17820

    Let’s assume the rate of interest in scheme A is ‘r’.

    17820 = 40500 of (100+r)% of (100+r)% - 40500

    17820 = 40500 [(100+r)% of (100+r)% - 1]

    0.44 = [(100+r)% of (100+r)% - 1]

    (100+r)% of (100+r)% = 1.44

    (100+r) (100+r) = 14400

    So the rate of interest in scheme A = r = 20%

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