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A sum of money becomes eight times in 3 years, if the rate is compounded annually. In how much time will the same amount at the same compound rate become thirty-two times?1). 6 years2). 4 years3). 8 years4). 5 years |
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Answer» ⇒ Let, Principal be RS. x then Amount = Rs. 8x, Rate = r% and TIME (n) = 3 years. ⇒ A = P × [1+ (r/100)]n ⇒ 8x = x × [1 +(r/100)]3 ⇒ 23 = [1+ (r/100)]3 ⇒ 2 = 1 + (r/100) ------ 1 ⇒ Amount becomes 16x then ⇒ A = P × [1+ (r/100)]n ⇒ 32X = x × [1+ (r/100)]n ⇒ putting the value from equation 1 we get ⇒ 32 = 2n ⇒ 25 = 2n ∴ n = 5 |
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