A man invested 1 3 of his capital at 7%; 1 4 at 8% and the remainder at 10%. If his annual income is Rs. 561, the capital is -

Answer: Option C

Let total capital be Rs. x
Then,
  $$\Rightarrow \left(\frac{x}{3}\times \frac{7}{100}\times 1\right)+\left(\frac{x}{4}\times \frac{8}{100}\times 1\right)+$$       $$\left(\frac{5x}{12}\times \frac{10}{100}\times 1\right)$$    $$=561$$
$$\begin{array}{rl}& \Rightarrow \frac{7x}{300}+\frac{x}{50}+\frac{x}{24}=561\\ & \Rightarrow 51x=\left(561\times 600\right)\\ & \Rightarrow x=\left(\frac{561\times 600}{51}\right)\\ & =6600\end{array}$$