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

Solution(By Examveda Team)

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

Alternate:
Rate = 10% = $$\frac{1}{{10}}$$
Let principal ⇒ (10)³ = 1000
Interest 1^st year → 100
Interest 2^nd year → 100 + 10
Interest 3^rd year = 100 + 10 + 10 + 1
C.I – S.I = 331 – 300 = 31
31 → 992
1 → 32
P → 32000