At what rate percent compound interest per annum will Rs 640

Let the rate of interest be $\mathrm{R} \%$.

Then,

$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$

$774.40=640\left(1+\frac{\mathrm{R}}{100}\right)^{2}$

$\left(1+\frac{\mathrm{R}}{100}\right)^{2}=\frac{774.40}{640}$

$\left(1+\frac{\mathrm{R}}{100}\right)^{2}=1.21$

$\left(1+\frac{\mathrm{R}}{100}\right)^{2}=(1.1)^{2}$

$\left(1+\frac{\mathrm{R}}{100}\right)=1.1$

$\frac{\mathrm{R}}{100}=0.1$

$\mathrm{R}=10$

Thus, the required rate of interest is $10 \%$ per annum.