A certain sum of money yields Rs. 1261 as compound interest for three years at 5% per annum. The sum is ?

Answer: Option D

Let the principal be x Rs. Now,
$$\begin{array}{rl}& C.I.=P\left[{\left(1+\frac{R}{100}\right)}^T-1\right]\\ & \Rightarrow 1261=x\left[{\left(1+\frac{5}{100}\right)}^3-1\right]\\ & \Rightarrow 1261=x\left(\frac{9261}{8000}-1\right)\\ & \Rightarrow 1261=x\left(\frac{9261-8000}{8000}\right)\\ & \Rightarrow 1261=\frac{1261x}{8000}\\ & \Rightarrow x=\frac{1261\times 8000}{1261}\\ & =\text{Rs}\text{.}8000\end{array}$$