Question

Ahmed buys a plot of land for Rs. 480000. He sells $\dfrac{2}{5}$ of it at a loss of 6%. At what gain per cent should he sell the remaining part of the plot to gain 10% on the whole?

Answer 1

Hint: We will first find the cost price and the selling price of the $\dfrac{2}{5}$ of land. Then, we will find the total amount of profit then Ahmed needs to sell the land at. We will find the cost price and the selling price of the remaining portion of the land and then apply the formula, $\dfrac{{{\text{Profit}}}}{{{\text{C}}{\text{.P}}{\text{.}}}} \times 100$ to calculate the gain percent. Here, profit is calculated by subtracting cost price from selling price.

Complete step-by-step answer:
We are given that the cost price of a land is Rs. 4,80,000. And Ahmed sells $\dfrac{2}{5}$ of it at a loss of 6%.
Let the total portion of the land be $x$.
Then , we can say the price of $x$ is Rs. 4,80,000.
We will now calculate the price of $\dfrac{2}{5}$ portion of land by multiplying it with the total cost of land.
$\Rightarrow$ $\dfrac{2}{5} \times 4,80,000 = 192000$
We are given that $\dfrac{2}{5}$ of total land is sold at a loss of 10%.
The amount of loss will be 6% of the cost price of land.
$\Rightarrow$ $\dfrac{6}{{100}} \times 192000 = 11520$
Hence, we can now calculate the selling price by subtracting the loss amount from the cost price.
$\Rightarrow$ $192000 - 11520 = 180480$
Now, we want the selling price of the remaining portion of the land should be such that there is a profit of 10% on the whole.
We will calculate the total selling price of the land if the profit is 10%
The profit amount will be 10% of 480000
$\Rightarrow$ \[\dfrac{{10}}{{100}} \times 4,80,000 = 48000\]
The total selling price will be $480000 + 48000 = 5,28,000$
From this, we already have the selling price of $\dfrac{2}{5}$ of land.
Then, the selling price of the remaining land $1 - \dfrac{2}{5} = \dfrac{3}{5}$ would be calculated by subtracting selling price of $\dfrac{2}{5}$ of land from the total selling price.
$\Rightarrow$ $528000 - 180480 = 347520$
We can also find the cost price of the remaining portion as $\dfrac{3}{5}$ of 480000
$\Rightarrow$ $\dfrac{3}{5} \times 480000 = 288000$
The profit amount selling the remaining portion should be $S.P. - C.P.$
$\Rightarrow$ $347520 - 288000 = 59,520$
It is known that profit percent is calculated using the formula, $\dfrac{{{\text{Profit}}}}{{{\text{C}}{\text{.P}}{\text{.}}}} \times 100$
Therefore, gain% on the remaining portion should be
$\dfrac{{59520}}{{288000}} \times 100 = 20.67\% $.

Note: We have calculated the selling price of $\dfrac{2}{5}$ portion of land by subtracting the amount of loss from the cost price. But, we can directly calculate $100 - 6 = 94\% $ of the cost price of the land which will also be equal to the selling price. And we consider the whole of the land as 1. Therefore, we subtracted $\dfrac{2}{5}$ from 1 to find the remaining portion of the land.