A man buys a field of agricultural land for Rs. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?

$$\eqalign{ & {\text{First}}\,{\text{Method}}: \cr & {\text{CP}} = 360000 \cr & {\text{To}}\,{\text{gain}}\,10\% \,{\text{on}}\,{\text{whole}}\,{\text{land}}, \cr & SP = 360000 + 10\% \,\text{of}\,360000 \cr & \,\,\,\,\,\,\,\, = Rs.\,396000 \cr & \frac{1}{3}\,{\text{of}}\,{\text{the}}\,{\text{land}}\,{\text{sold}}\,{\text{on}}\,20\% \,{\text{loss}}. \cr & {\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{land}} \cr & = {\frac{{360000}}{3}} - 20\% \,{\text{of}}\,\, {\frac{{360000}}{3}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}\,{\text{of}}\,{\text{the}}\,{\text{land}} \cr & = \frac{{ {360000 \times 2} }}{5} + 25\% \,{\text{of}}\,\,\frac{{ {360000 \times 2} }}{5} \cr & = Rs.\,180000 \cr & {\text{Thus}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{land}} \cr & = 396000 - 96000 - 180000 \cr & = Rs.\,120000 \cr & \cr & {\text{Second}}\,{\text{Method:}} \cr & {\text{SP of total agricultural }} \cr & {\text{field at a profit of}} \cr & 10\% = \frac{{ {360000 \times 110} )}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\, = Rs.\,396000 \cr & {\text{So,}}\,{\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{of}}\,{\text{field}} \cr & = {\frac{{360000}}{3}} \times {\frac{{80}}{{100}}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}th\,{\text{of}}\,{\text{the}}\,{\text{field}} \cr & = \frac{{ {2 \times 360000 \times 125} }}{{ {5 \times 100} }} \cr & = Rs.\,180000 \cr & {\text{Hence}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{field}} \cr & = Rs.\,\left( {396000 - 96000 - 180000} \right) \cr & = Rs.\,120000 \cr} $$