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If the compound interest on a certain sum for 2 years at 3% p.a. is Rs 101.50, then what will be the simple interest on the same sum at the same rate and for the same time ?

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Let the principal be Rs P. Then,

101.50 = P\(\Big[\big(1+\frac{3}{100}\big)^2-1\Big]\) = P\(\Big[\big(\frac{103}{100}\big)^2-1\Big]\)

\(\Rightarrow\) 101.50 = P\(\Big[\frac{(103)^2-(100)^2}{10000}\Big]\) = P\(\Big[\frac{(103+100)(103-100)}{10000}\Big]\)

\(\Rightarrow\) P= \(\frac{101.50\times10000}{203\times3}\) = Rs\(\frac{5000}{3}\)

\(\therefore\) S.I = \(\frac{5000\times3\times2}{3\times100}\) = Rs 100.

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