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    Question

    The compound interest received on investing Rs. 10,000

    for 2 years at 'y'% p.a., compounded annually is Rs. 3,689. The simple interest earned on investing Rs. 'K' for 2 years at (y + 3)% p.a. is Rs. 181 more than the compound interest received on investing Rs. (K + 400) for 2 years at (y − 2)% p.a., compounded annually. Find the value of 'K'. 
    A 3600 Correct Answer Incorrect Answer
    B 4200 Correct Answer Incorrect Answer
    C 4000 Correct Answer Incorrect Answer
    D 4400 Correct Answer Incorrect Answer
    E 3800 Correct Answer Incorrect Answer

    Solution

    Compound interest received on investing Rs. 10,000
    = Rs. [10000 × {1 + (y/100)}2 − 10000]
    So, [10000 × {1 + (y/100)} 2 − 10000] = 3689
    Or, 10000 × {(100 + y)/100}2 = 10000 + 3689 = 13689
    Or, {(100 + y)/100}2 = 13689 ÷ 10000 = 1.3689
    So, {(100 + y)/100} = √1.3689 = 1.17
    So, 100 + y = 117
    So, y = 17
    Simple interest received on investing Rs. 'K'   = K × (17 + 3) × 2 ÷ 100 = Rs. 0.4K
    Compound interest received on investing Rs. (K + 400)
    = (K + 400) × {1 + (15/100)}2 − (K + 400)
    = (K + 400) × 1.3225 − (K + 400)
    = Rs. (0.3225K + 129)
    According to the question,
    0.4K = (0.3225K + 129) + 181
    Or, 0.0775K = 310
    So, K = 310 ÷ 0.0775 = 4000

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