Question

A plot is sold for Rs. 18,700 with a loss of 15%. At what price should it be sold to get profit of 15%?
A. Rs. 25300
B. Rs. 54000
C. Rs. 25600
D. Rs. 25900

Answer 1

Hint: First assume the actual price of the plot as X. Now find the actual price of plot using the formula \[\text{X-}\dfrac{\text{ }\!\!\%\!\!\text{ loss}}{\text{100}}\text{ }\!\!\times\!\!\text{ X=selling price}\] . And after finding actual price, use the formula \[\text{X+}\dfrac{\text{ }\!\!\%\!\!\text{ profit}}{\text{100}}\text{ }\!\!\times\!\!\text{ X}\] to get the profit in selling the plot.

Complete step by step solution:
We are given that the plot is sold for Rs. 18,700, for which there is a loss of 15%.
Let us assume that the actual price of the plot is X which is nothing but the cost price.
It is sold with a loss of 15%, so we can write the formula as
\[X-\dfrac{15}{100}\times X=18700\]
Taking the LCM of terms on the LHS and subtracting, we get
\[\dfrac{85}{100}X=18700\]
After simplifying, we get
\[X=\dfrac{18700\times 100}{85}\]
\[X=22000\]
So the actual price of the plot is Rs. 22,000.
Now to gain profit, the selling price must be greater than the actual price.
We know that the actual price is Rs. 22000. So, to gain the profit of 15%, the selling price should be
\[X+X\times \dfrac{15}{100}\]
Taking the LCM of terms and adding, we get
\[\dfrac{115}{100}X\]
Now putting the value of X, we have
\[\dfrac{115}{100}\times 22000\]
Rs. 25,300
So the price for which the plot should be sold to gain 15% profit = Rs. 25,300.
Hence the correct option is (A).

Note: The possibility for the mistake is that students can make the mistake in calculating the actual price of the plot. They can use the formula \[18700-18700\times \dfrac{15}{100}=X\] which may lead to wrong answers. As from this formula we get X less than 18700 but for the loss, the cost price/actual price must be greater than Rs. 18700.