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    Question

    (Q.126-130): Study the following information carefully and answer the Questions given below:

    Quantity I. A sum of money becomes double in 4 years at

    compound interest, compounded annually. In how many years it will become 9 times? Quantity II. A sum of money tripled itself in 20 years at a certain rate of interest. In how many years the amount would have been 1.5 times of itself at the same rate of interest?
    A Quantity I < Quantity II Correct Answer Incorrect Answer
    B Quantity I > Quantity II Correct Answer Incorrect Answer
    C Quantity I ≤ Quantity II Correct Answer Incorrect Answer
    D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    E Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer

    Solution

    Quantity I. A=   p [1+`R/100` ]t         ⇒ 3P = P [1+`R/100` ]4 ⇒ 3 = [1+ `R/100` ]4 …………(i) A= p [1+`R/100` ]t ⇒ 9P = P [1+`R/100` ]t ⇒ 32 = [1+ `R/100` ]t …………….(ii) From (i) and (ii)  [1+`R/100` ]4 × 2 = [1+`R/100` ]t t = 8 years Quantity II. Since the amount was Rs 100. It becomes Rs 300 in 20 years. Rs 300 – Rs 100 = Rs 200 interest In 20 years, interest is Rs 200 In 1 year, the interest is Rs`200/20` Rate of interest = 10% per annum.  = 100 x 50 / 100 x 10 = 5 years Hence Quantity I > Quantity II

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