If the simple interest and compound interest at the same rate of certain amount for 2 years are Rs. 400 and Rs. 420 respectively, then the rate of interest is ;

Principal = Rs. P, Rate = R% per annum S.I

$=\frac{\text { Principal } \times \text { Time } \times \text { Rate }}{100}$

$\Rightarrow 400=\frac{\mathrm{P} \times 2 \times \mathrm{R}}{100}=\frac{\mathrm{PR}}{50}$

$\Rightarrow \mathrm{PR}=$ Rs. $(400 \times 50)=$ Rs. $20000 \ldots \ldots$ (i)

Again,

C.I. – S.I. = Rs. (420 – 400) = Rs. 20

$\therefore \quad$ Difference $=\frac{\mathrm{PR}^{2}}{10000}$

⇒ 20 × 10000 = PR² ..... (ii)

On dividing equation (ii) by (i)

$\frac{20 \times 10000}{20000}=\mathrm{R}$

$\Rightarrow \mathrm{R}=10 \%$ per annum