A certain sum of money double itself in 8 years. In how much time will it become 4 times of itself at the same rate of interest.

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Solution

$Let the sum of money = Rs x Time, T = 8 yrs Now, Amount = Rs 2 x Now, SI = \frac{PRT}{100} \Rightarrow A - P = \frac{PRT}{100} \Rightarrow 2 x - x = \frac{x \times R \times 8}{100} \Rightarrow x = \frac{2 Rx}{25} \Rightarrow R = \frac{25}{2} So, rate of interest = R = \frac{25}{2} % p . a . Suppose it becomes 4 times of itself in y yrs . Now, Amount, A_{1} = Rs 4 x Time, T = yrs Rate, R = \frac{25}{2} % p . a . SI = \frac{PRT}{100} \Rightarrow A_{1} - P = \frac{PRT}{100} \Rightarrow 4 x - x = \frac{x \times 25 \times y}{200} \Rightarrow 3 = \frac{25 y}{200} \Rightarrow y = 24 So, required time is 24 yrs .$

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