The difference between simple interest ans compound interest on Rs. P at R% p.a in 2 years is = ?

1Rs. ^PR/₁₀₀
2Rs. ^2PR/₁₀₀
3Rs. ^PR²/₁₀₀
4Rs. ^PR²/_(100)²

Answer:- 1

Explanation:-

Solution:

\begin{aligned} S .I . =  Rs . (\frac{P \times R \times 2}{100}) \\ = Rs . (\frac{2 P R}{100}) \\ C .I . =  Rs . [P \times {(1 + \frac{R}{100})}^{2} - P] \\ = Rs . [\frac{P R^{2}}{{(100)}^{2}} + \frac{2 P R}{100}] \\ ∴ Difference \\ =  Rs . [{\frac{P R^{2}}{{(100)}^{2}} + \frac{2 P R}{100}} - \frac{2 P R}{100}] \\ = Rs . [\frac{P R^{2}}{{(100)}^{2}}] \end{aligned}

$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{P \times R \times 2}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left( {\frac{{2PR}}{{100}}} \right) \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {P \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - P} \right] \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right] \cr & \therefore {\text{Difference}} \cr & {\text{ = Rs}}{\text{.}}\left[ {\left\{ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right\} - \frac{{2PR}}{{100}}} \right] \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}} \right] \cr}$