Question

If the principal is doubled, what change must be made in the rate of interest such that the interest is the same through out?

Answer 1

We know that,
$\frac{interest}{principal}$ = $\frac{rate}{100}$
$\to$ interest = $\frac{principal\times rate}{100}$
For the principal P and 2P, let the rate of interest be $R_1$ and $R_2$, and the interest be $I_1$ and $I_2$.
$\mathrm{Therefore},I_1=\frac{{\mathrm{PR}}_1}{100}\mathrm{and}{I}_2=\frac{2{\mathrm{PR}}_2}{100}\mathrm{Given},I_1=I_2\Rightarrow \frac{{\mathrm{PR}}_1}{100}=\frac{2{\mathrm{PR}}_2}{100}\Rightarrow R_2=\frac{R_1}{2}$