Question

A sum of rs. 8000 becomes rs. 9261 in 3 years compounded annually at a certain rate. Find the rate percent.

Answer 1

$let \: rate\% \: be \: r \: \\ principal = 8000 \: rupees \\ amount = 9261 \: rupees \\ time = 3 \: years \\ \\ amount = p(1 + \frac{r}{100}) {}^{n } \\ \\ = > 9261 = 8000(1 + \frac{r}{100} ) {}^{3} \\ \\ = > \frac{9261}{8000} = (1 + \frac{r}{100} ) {}^{3} \\ \\ here \: 9261 \: is \: the \: perfect \: cube \: of \\ 21 \: and \: 8000 \: is \: the \: perfect \: cube \: \\ of \: 20 - - \\ \\ = > (\frac{21}{20} ) {}^{3} =( 1 +\frac{r}{100}) {}^{3} \\ \\ taking \: cube \: root \: both \: sides - - \\ \\ = > \sqrt[3] { (\frac{21}{20})^{3}} = \sqrt[3]{(1 + \frac{r}{100}) {}^{3} } \\ \\ = > \frac{21}{20} = 1 + \frac{r}{100} \\ \\ = > \frac{21}{20} - 1 = \frac{r}{100} \\ \\taking \:LCM\\\\ = > \frac{21 - 20}{20} = \frac{r}{100} \\ \\ = > \frac{1}{20} = \frac{r}{100} \\ \\ = > \frac{1}{20} \times 100 = r \\ \\ = > 5 = r \\ \\ so \: \: the \: rate \: \% \: per \: annum \: is \: 5\% \\ \\ \\ please \: mark \: it \: as \: brainliest.$