A man buys land for Rs 3,00,000. He sells 1/3rd of it at a loss of 20% and 2/5th of the plot at a gain of 25%. At what price should he sell the remaining land so as to make an overall profit of 10%?

Given: A man buys land for Rs 3,00,000.

He sells $\frac{1}{3}$ of it at a loss of 20% and $\frac{2}{5} $ at a gain of 25%.

To do: At what price should he sell the remaining land so as to make an overall profit of 10%

Solution:

Cost price of total land = CP = 3,00,000

CP of $\frac{1}{3}$rd land = $\frac{1}{3} \times 3,00,00 = 1,00,000$

SP at a loss of 20% = $1,00,000 \times \frac{100 - 20}{100}$

                                  =  $1,00,000 \times \frac{80}{100}$

                                  = 80,000

CP of $\frac{2}{5}$ th land = $\frac{2}{5} \times 3,00,00 = 1,20,000$

SP at a gain of 25% = $1,20,000 \times \frac{100 + 25}{100}$

                                    =  $1,20,000 \times \frac{125}{100}$

                                    =$1200 \times 125$

                                     = $1,50,000$

CP or remaining land = $3,00,000 - 1,00,000 -1,20,000$ = 80,000 

Overall 10% gain on CP or 3,00,000

SP = $3,00,000 \times \frac{100 + 10}{100} =3,30,000$

He should sell the remaining plot at

$3,30,000 -  80,000 - 1,50,000 = 1,00,000$

 He should sell the remaining plot at

Rs 1,00,000 so that he gains overall 10%