Question

Tick (✓) the correct answer:
If the compound interest on a sum for 2 years at $12\frac{1}{2}\%$ per annum is Rs 510, the simple interest on the same sum at the same rate for the same period of time is
(a) Rs 400
(b) Rs 450
(c) Rs 460
(d) Rs 480

Answer 1

(d) Rs 480

$$\begin{gathered} \mathrm{We}\mathrm{have}:510=\left\{P\times {\left(1+\frac{25}{100\times 2}\right)}^2\right\}-P \\ \Rightarrow 510=\Rightarrow \left\{P\times {\left(\frac{8+1}{8}\right)}^2\right\}-P \\ \Rightarrow 510=\left\{P\times \left(\frac{9}{8}\right)\times \left(\frac{9}{8}\right)\right\}-P \\ \Rightarrow 510=\left(\frac{81\mathrm{P}}{64}-\mathrm{P}\right) \\ \Rightarrow 510=\left(\frac{81\mathrm{P}-64\mathrm{P}}{64}\right) \\ \Rightarrow 510=\frac{17P}{64} \\ \therefore P=\frac{510\times 64}{17}=\mathrm{Rs}1920 \\ \mathrm{Now},\mathrm{SI}=\frac{P\mathit{\times }R\mathit{\times }T}{100} \\ =\mathrm{Rs}\frac{1920\times 2\times 25}{100\times 2}=\mathrm{Rs}480 \end{gathered}$$