Question

When the plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
(a) Rs. 21,000
(b) Rs. 22,500
(c) Rs. 25,300
(d) Rs. 25,800

Answer 1

Hint: We start solving the problem by assuming the variable for the cost of the plot that the owner has bought. We then use the fact that the owner has to sell the plot 15% less than the cost of the plot to incur a 15% loss. We then make use of the formula that a% of b is defined as $ \dfrac{a}{100}\times b $ to get the value of c. We then use the fact that the owner has to sell the plot 15% more than the cost of the plot to incur a 15% gain to get the required answer.

Complete step by step answer:
According to the problem, we are given that the owner loses 15% if the plot sold for Rs. 18,700. We need to find the price at which the plot must be sold in order to gain 15%.
Now, let us assume that the cost price of the plot that the owner bought is ‘c’.
We have given that the owner loses 15% if he sells the plot for Rs. 18,700. This tells us that Rs. 18,700 is 15% less than the cost that the owner had bought.
So, we have $ \left( 100-15 \right)\%\Leftrightarrow 85\% $ of c = Rs. 18,700.
We know that a% of b is defined as $ \dfrac{a}{100}\times b $ .
 $ \Rightarrow \dfrac{85}{100}\times c=18700 $ .
 $ \Rightarrow c=18700\times \dfrac{100}{85} $ .
 $ \Rightarrow c=Rs.22000 $ .
So, we have found that the owner bought the plot for Rs. 22,000.
Now, we need to find the price at which the owner needs to sell the plot in order to gain 15%.
We know that the owner has to sell the plot 15% more than the price he bought. This means that the owner has to sell the plot for $ \left( 100+15 \right)\%\Leftrightarrow 115\% $ of c.
So, we get the selling price of the plot as $ \dfrac{115}{100}\times 22000=25300 $ .
Hence, the owner had to sell the plot for Rs. 25,300 to gain 15%.
 $ \therefore, $ The correct option for the given problem is (c).

Note:
We should not confuse a% of b with $ a\times b $ instead of $ \dfrac{a}{100}\times b $ which is the most common mistake done by students. We should not make calculation mistakes while solving this problem. We can also make use of the fact $ profit\left( or \right)loss\%=\dfrac{\text{selling price}-\text{cost price}}{\text{cost price}}\times 100 $ to avoid confusions. Similarly, we can expect problems to find the gain or loss percentage if the owner sold the plot for Rs. 26,400.