The compound interest on a certain sum of money for 2 years at 5% per annum is Rs 410. The simple interest on the same sum at the same rate and for the same time is = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Rate of interest 5}}\% \cr & = \frac{1}{{20}} \cr & {\text{Let principal}} \cr & {\text{ = }}{\left( {20} \right)^2}{\text{ = 400 units}} \cr & \Rightarrow {\text{ Total compound interest }} \cr & {\text{41 Units }} \to {\text{Rs. 410 }} \cr & {\text{1 Units }} \to {\text{Rs. 10 }} \cr & {\text{400 Units }} \to {\text{Rs. 400 }} \cr & {\text{Total simple interest}} \cr & {\text{ = Rs. 400}} \cr} $$

Alternate
Total compound interest for 2 years at 5% p.a.
$$\eqalign{ & {\text{ = 5 + 5 + }}\frac{{5 \times 5}}{{100}} = 10.25\% \cr & {\text{Total simple interest}} \cr & = 10\% \cr & \Rightarrow 10.25\% \to 410 \cr & \Rightarrow 10\% \to 400 \cr & {\text{Simple interest}} \cr & {\text{ = Rs}}{\text{. 400}} \cr} $$