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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 =

a) Rs. 400
b) Rs. 300
c) Rs. 350
d) Rs. 405

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

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