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    Question

    Rajat invested Rs. (P-100) on compound interest at the

    rate of ‘R’ % per annum compounded annually. Ravi invested Rs. (P+300) on simple interest at the rate of (R-2) % per annum. Rehan invested Rs. (P-500) at the rate of 27% per annum on simple interest and at the end of three years, he got Rs. 4860 as an interest. If at the end of two years, the interest obtained by Rajat is 368 more than the interest obtained by Ravi, then find out the value of ‘R’.
    A 18 Correct Answer Incorrect Answer
    B 21 Correct Answer Incorrect Answer
    C 15 Correct Answer Incorrect Answer
    D 30 Correct Answer Incorrect Answer
    E None of the above Correct Answer Incorrect Answer

    Solution

    Rehan invested Rs. (P-500) at the rate of 27% per annum on simple interest and at the end of three years, he got Rs. 4860 as an interest.

    (P-500)x27%x3 = 4860

    (P-500)x81% = 4860

    (P-500) = 486000/81

    (P-500) = 6000

    P = 6000+500

    P = 6500

    Rajat invested Rs. (P-100) on compound interest at the rate of ‘R’ % per annum compounded annually. Ravi invested Rs. (P+300) on simple interest at the rate of (R-2) % per annum. If at the end of two years, the interest obtained by Rajat is 368 more than the interest obtained by Ravi.

    (P-100)[(1+(R/100))2-1] = [(P+300)x(R-2)x2]/100 + 368

    Put the value of ‘P’ in the above equation.

    (6500-100)[(1+(R/100))2-1] = [(6500+300)x(R-2)x2]/100 + 368

    6400[(1+(R/100))2-1] = [6800x(R-2)x2]/100 + 368

    After solving the above equation, we will get a quadratic equation which is given below.

    64R2-800R-9600 = 0

    2R2-25R-300 = 0

    2R2-(40-15)R-300 = 0

    2R2-40R+15R-300 = 0

    2R(R-20)+15(R-20) = 0

    (R-20) (2R+15) = 0

    R = 20, -(15/2) As we know that the negative value of ‘R’ is not possible. So the value of ‘R’ is 20 .

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