Two - thirds of a consignment was sold at a profit of 6% and the rest at a loss of 3%. If however there was an overall profit of Rs. 540, the value of consignment was -

Explanation:-

Let the total value be Rs. x $$\eqalign{ & {\text{value of }}\frac{2}{3}{\text{rd}} = {\text{Rs}}{\text{.}}\frac{{2x}}{3}, \cr & {\text{value of}}\frac{1}{3}{\text{rd}} = {\text{Rs}}.\frac{x}{3}. \cr & {\text{Total S}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left[ {\left( {106\% {\text{ of }}\frac{{2x}}{3}} \right) + \left( {97\% {\text{ of }}\frac{x}{3}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{53x}}{{75}} + \frac{{97x}}{{300}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{309x}}{{300}}} \right). \cr & \therefore \frac{{309x}}{{300}} - x = 540 \cr & \Rightarrow \frac{{9x}}{{300}} = 540 \cr & \Rightarrow x = \left( {\frac{{540 \times 300}}{9}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 18000. \cr}$$