Question

Amla bought a house for some amount of money. She spent Rs sixty thousand on remodeling her house. After some time, she sold her house at the profit of 20 %. If she sells the house for Rs forty two lakhs, then find the cost at which she bought the house.

Answer 1

Hint: First calculate the total cost of house she expends on the house just before selling her house for Rs forty two lakhs at a profit of 20 % using the formula:

Profit percentage = $\dfrac{\text{Selling price - Cost price}}{\text{Cost price}}\times 100%$
In this formula Selling price is given as Rs forty two lakhs, profit percentage is given 20 %, only one variable left which can be found out.
In the cost price found using the above formula, remodeling cost is also included. So to find the cost at which she bought the house, subtract the remodeling cost from the calculated cost price.



Complete step-by-step answer:

If person bought something for some money say Cost Price and sell it at some profit for some money say Selling Price, then his profit percentage is calculated by
Profit percentage = $\dfrac{\text{Selling Price - Cost Price}}{\text{Cost Price}}\times 100%\,\,\,\,\,\,\,\,\,\,\cdot \cdot \cdot \text{(i)}$
It is given that Amla sold her house for Rs 4200000 at a profit of 20 %.
So Selling price = Rs 4200000
Profit percentage = 20 %
Now using the equation (i) we calculate the cost she expends just before selling her house.
$\begin{align}
  & 20=\dfrac{4200000-\text{Cost Price}}{\text{Cost Price}}\times 100 \\
 & \Rightarrow \dfrac{20}{100}=\dfrac{4200000}{\text{Cost Price}}-1 \\
 & \Rightarrow \dfrac{1}{5}+1=\dfrac{4200000}{\text{Cost Price}} \\
 & \Rightarrow \dfrac{\text{Cost Price}}{4200000}=\dfrac{5}{6} \\
 & \Rightarrow \text{Cost Price}=4200000\cdot \dfrac{5}{6}=3500000 \\
\end{align}$
So Rs 3500000 is the expenditure on a house by Amla. In this cost, remodeling cost is included which is Rs 60000. Subtracting this cost will give us the amount of money she spent in buying the house.
Cost at which she bought the house = Rs 3500000 – Rs 60000 = Rs 3440000.
Hence, she bought the house for Rs 3440000.

Note: One can make mistake in using the formula as
Profit percentage = $\dfrac{\text{Cost Price - Selling Price}}{\text{Cost Price}}\times 100%$
This formula will give the wrong result as this formula is used when loss is incurred in a transaction and our question is of profit.