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The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs. 283.50. Find the sum.

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Best answer

Given, 

Rate = 15 % p.a 

Time = 3 years 

C.I – S.I = Rs.283.50 

Let principal = P 

So,

\(={P}[({1}+\frac{15}{100})^3-{1}]-\frac{P \times 15 \times 3}{100}\) = 283.50

\(={P}(\frac{23}{20})^3-{1}]-\frac{9p}{20}\) = 283.50

\(=\frac{4167p-3600p}{800}\) = 283.50

\(={567p}={283.50\times800}\) 

\(={p}=\frac{283.50\times800}{567}\) = Rs. 4000

Hence, 

Principal = Rs. 4000

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