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

Answer: Option D

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

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