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The difference between CI and SI for 3 years Rs. 992. If rate of interest is 10%. Find the Principal ?

a) Rs. 22000
b) Rs. 30000
c) Rs. 28000
d) Rs. 32000

Answer: d
Explanation:
$$\eqalign{ & {\text{Rate}} = 10\% ,\, \cr & {\text{Let}}\,{\text{Principal}} = P \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times 10 \times 3}}{{100}} = \frac{{3P}}{{10}} \cr & {\text{C}}{\text{.I}}{\text{.}} = P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} – 1} \right\} \cr & {\text{C}}{\text{.I}}{\text{.}}\,\, – \,\,{\text{S}}{\text{.I}}{\text{.}} = 992 \cr & P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} – 1} \right\} – \frac{{3P}}{{10}} = 992 \cr & P\left\{ {{{\left( {\frac{{11}}{{10}}} \right)}^3} – 1 – \frac{3}{{10}}} \right\} = 992 \cr & P\left\{ {\frac{{\left( {1331 – 1000 – 300} \right)}}{{1000}}} \right\} = 992 \cr & P\left( {\frac{{31}}{{1000}}} \right) = 992 \cr & P = 32000 \cr} $$

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