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      Question

      Under compound interest, an amount doubles in 3 years.

      How many years will it be 256 times its amount?
      A 24 years Correct Answer Incorrect Answer
      B 28 years Correct Answer Incorrect Answer
      C 22 years Correct Answer Incorrect Answer
      D 26 years Correct Answer Incorrect Answer

      Solution

      Let the principal be Rs. x Amount = 2x As we know, A = P (1 + r/100) t     2x = x (1 + r/100)3 (1+r/100) = 3√2 ----(i) Again, A = 256x, P = x, Time = t years (suppose) 256x = x (1 + r/100) =(1+r/100) = √256 ----(ii) From equation (i) and (ii), we get 3√2 = 256 21/3 = 288/t Compare on powers 1/3 = 8/t t = 24 years Smart Approach. 3year =2times X year =256 times=28   X=3×8 =24years.

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