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The difference in simple interest and compound interest on a certain sum of money at 6 2/3 % per annum for 3 years in Rs. 46. Determine the sum.

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Given, 

S.I – C.I = Rs. 46 

Rate \({6}\frac{2}{3}\text%\) \(=\frac{20}{3}\text%\) per annum

Time = 3 years 

Let principal = Rs. P 

So,

\(\frac{P \times 3 \times 20}{3\times100}-{P}[({1}+\frac{20}{300})^3-{1}]\) = 46

\(=\frac{P}{5}-\frac{721P}{3375}\) = 46

\(=\frac{675P-721P}{3375}\) = 46

\(={P}=\frac{3375\times46}{46}\) = Rs.3375

Hence, 

Principal = Rs. 3375

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