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Aman invests $\mathrm{Rs} \: 4000$ in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after $3$ years to the value of the investment after $5$ years is $25: 36$, then the minimum number of years required for the value of the investment to exceed $\mathrm{Rs} \: 20000$ is

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