Question

A man buys a plot of agricultural land for Rs. 300000. 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 land so as to make an overall profit of \[10\% \].

Answer 1

Hint:
Here we will first find the final selling price of the land so as to make a profit of \[10\% \]. Then we will find the selling price of one-third of the land with the given conditions of loss. Then we will find the value of the two-fifths of the land with the given condition of profit. Further, we will subtract the selling price of one-third of the land and selling price of the two-fifth of the land from the final selling price of the land to get the selling price of the remaining land.

Complete Step by Step Solution:
It is given that a man buys a plot of agricultural land for Rs. 300000.
First, we will find the value of the total selling price of the agricultural land with the profit of \[10\% \]. Therefore, we get
Final selling price of the agricultural area \[ = 300000 + \left( {\dfrac{{10}}{{100}} \times 300000} \right) = Rs.330000\]……………………. \[\left( 1 \right)\]
It is given that he sells one-third of the land at a loss of \[20\% \].
So, we will find the actual price of this land.
Actual price of one-third of the land \[ = \dfrac{1}{3} \times 300000 = {\rm{Rs}}.100000\]
Now, we will find the selling price of this one-third of the land.
Selling price of the one-third of the land \[ = 100000 - \left( {\dfrac{{20}}{{100}} \times 100000} \right) = Rs.80000\]…………………… \[\left( 2 \right)\]
It is also given that he sells two-fifths at a gain of \[25\% \]. We will find the actual price of this two-fifth of the land, we get
Actual price of two-fifth of the land \[ = \dfrac{2}{5} \times 300000 = Rs.120000\]
So we will find the selling price of this two-fifth of the land. Therefore, we get
Selling price of the two-fifth of the land \[ = 120000 + \left( {\dfrac{{25}}{{100}} \times 120000} \right) = Rs.150000\]…………………… \[\left( 3 \right)\]
Now we will subtract the selling price of the one-third of the land and the selling price of the two-fifth of the land from the final selling price of the land to get the selling price of the remaining land. Therefore subtracting the equation \[\left( 2 \right)\] and equation \[\left( 3 \right)\] from the equation \[\left( 1 \right)\], we get
Selling price of the remaining land \[ = 330000 - 80000 - 150000 = Rs.100000\]

Hence he must sell the remaining land at the rate of Rs. 100000 so as to make an overall profit of \[10\% \].

Note:
Selling price is the price at which something is sold. Cost price is the cost of producing something or the price at which it is sold without making any money. Profit is the money that you make when you sell something for more than it cost you and loss is the money you make when you sell something for less than it cost you. Revenue of a product is equal to the total amount generated by selling the product at some selling price. If the revenue generated by the company is less than the total cost of production then there is loss to the company rather than profit.