Question

A man buys a plot of land at Rs3,00,000. He sells one-third of the plot at a loss of 20%. Again, he sells two-fifth of the plot left at a profit of 25%. At what price should he sell the remaining plot in order to get a profit of 10% on the whole?

Answer 1

Hint: Use the selling price formula \[{\text{S}}{\text{.P}} = {\text{C}}{\text{.P}} \times \left( {1 - \dfrac{{{\text{loss}}\% }}{{100}}} \right)\] to find the selling price of one-third land then use \[{\text{S}}{\text{.P}} = {\text{C}}{\text{.P}} \times \left( {1 + \dfrac{{{\text{profit}}\% }}{{100}}} \right)\] to find the selling price of two-fifth land and whole land at 10% profit. After this, subtract the selling price of one-third of the land and two-fifth land from the selling price of the whole land at 10% profit.

Complete step by step answer:
We know the cost price of the total land is Rs. $3,00,000$.

From the whole land, one-third is sold. We can find the cost price of one-third by taking one-third of the total cost.

Take one-third of the total cost as

\[\dfrac{1}{3} \times 3,00,000 = 1,00,000\]

Thus, the cost price of a one-third portion of the land is Rs $1,00,000$.

As we know that one-third of the land is sold in loss so, we can apply the formula \[{\text{S}}{\text{.P}} = {\text{C}}{\text{.P}} \times \left( {1 - \dfrac{{{\text{loss}}\% }}{{100}}} \right)\] to find the selling price of the one-third land in 20% loss.
We are substituting the values \[{\text{C}}{\text{.P}} = 1,00,000\] and \[{\text{loss}}\% = 20\] into the formula,

\[{\text{S}}{\text{.P}} = {\text{C}}{\text{.P}} \times \left( {1 - \dfrac{{{\text{loss}}\% }}{{100}}} \right)\], we get,

\[
  {\text{S}}{\text{.P}} = {\text{1,00,000}} \times \left( {1 - \dfrac{{20}}{{100}}} \right) \\
   = {\text{1,00,000}} \times \left( {\dfrac{{100 - 20}}{{100}}} \right) \\
   = {\text{1,00,000}} \times \left( {\dfrac{{80}}{{100}}} \right) \\
   = {\text{10,000}} \times 8 \\
   = 80,000 \\
 \]

Thus, the selling price of the one-third land is $Rs.80,000$.

Again, two-fifth of the remining plot is sold in profit of 25%. Now we will find the cost price of two-fifth of the land by taking two-fifth of the total cost.
The remaining plot is $\dfrac{2}{3}$.
Take two-third of the total cost as

\[\dfrac{2}{3} \times 3,00,000 = 2,00,000\]
The cost price for the two-fifth of the remining plot is,
$\dfrac{2}{5} \times 2,00,000 = 80,000$

Thus, the cost price of the two-fifth portion of the land is Rs $80,000$.

As we know that two-fifth of the land is sold in profit so, we can apply the formula \[{\text{S}}{\text{.P}} = {\text{C}}{\text{.P}} \times \left( {1 + \dfrac{{{\text{profit}}\% }}{{100}}} \right)\] to find the selling price of the two-fifth land.

We are substituting the values \[{\text{C}}{\text{.P}} = 80,000\] and \[{\text{profit}}\% = 25\] into the above formula, we get,

\[
  {\text{S}}{\text{.P}} = 8{\text{0,000}} \times \left( {1 + \dfrac{{25}}{{100}}} \right) \\
   = 80,{\text{000}} \times \left( {\dfrac{{100 + 25}}{{100}}} \right) \\
   = 8{\text{0,000}} \times \left( {\dfrac{{125}}{{100}}} \right) \\
   = 8{\text{00}} \times 125 \\
   = 1,00,000 \\
 \]

Thus, the selling price of the two-fifth land is Rs $1,00,000$.

Now we want a total of 10% profit on the whole land. For this, we can find the total selling price at 10% profit and then subtract the cost price of one-third of the land and two fifth land.

Substituting the values \[{\text{C}}{\text{.P}} = 3,00,000\] and \[{\text{profit}}\% = 10\] into the above formula\[{\text{S}}{\text{.P}} = {\text{C}}{\text{.P}} \times \left( {1 + \dfrac{{{\text{profit}}\% }}{{100}}} \right)\] to find the total selling price of the whole land at 10% profit.

\[
  {\text{S}}{\text{.P}} = {\text{3,00,000}} \times \left( {1 + \dfrac{{10}}{{100}}} \right) \\
   = {\text{3,00,000}} \times \left( {\dfrac{{100 + 10}}{{100}}} \right) \\
   = {\text{3,00,000}} \times \left( {\dfrac{{110}}{{100}}} \right) \\
   = {\text{3,000}} \times 110 \\
   = 3,30,000 \\
 \]

Thus, the total selling price of the land at 10% profit is Rs $3,30,000$.

But our task is to find the selling price of the reaming land, so, to reach our task we are subtracting the above-obtained selling price of one-third land and two-fifth land from the total selling price of the land,
Therefore, selling price of the remaining land would be,

\[
   = 3,30,000 - 80,000 - 1,00,000 \\
   = 1,50,000 \\
 \]

Therefore, the selling price of the remaining land is $Rs.1,50,000$.

Note:
Profit and loss are calculated on the cost price of the thing.
One-third of any amount is computed by multiplying the amount by one-third. Similarly, two-fifth of the remaining land amount is computed by multiplying the amount by the two-fifth and the part of the land which remains left and has to be sold.