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

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