Question

Mr. Virmani purchased a house for Rs. 365000 and spent Rs. 135000 on its repairs. If he sold it for Rs. 550000, find his gain percent.

Answer 1

Hint:
Here, we need to find the gain percent on the sale of the house. We will use the concept of cost price, selling price, and gain to solve this question. Cost price is defined as the price at which the object is purchased. Selling price is the price at which the object is sold. The gain or profit is defined as the difference in selling price and cost price. We will find the cost price by adding the cost of purchase and repair costs. Then we will find out the gain by subtracting the cost price from the selling price. We will then use the formula of gain percent to find the answer.
Formula Used: The gain on the sale of an object is given by
\[{\text{Gain}} = {\text{S}}{\text{.P}}{\text{.}} - {\text{C}}{\text{.P}}{\text{.}}\], where \[{\text{S}}{\text{.P}}{\text{.}}\] is the selling price of the object and \[{\text{C}}{\text{.P}}{\text{.}}\] is the cost price of the object. The gain percent is given by \[{\text{Gain Percent}} = \dfrac{{{\text{Gain}}}}{{{\text{C}}{\text{.P}}{\text{.}}}} \times 100\].

Complete step by step solution:
The cost price of an object is the total cost of the object, including the purchase cost, cost of repairs, cost of installation, etc.
We can find the cost of price by adding the cost of purchase of the house and the cost of repairs.
Therefore, we get
\[\begin{array}{l}{\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}365000 + {\text{Rs}}{\text{. }}135000\\ = {\text{Rs}}{\text{. }}500000\end{array}\]
Thus, the cost price of the house is Rs. 500000.
The selling price of an object is the price at which the object is sold at.
Therefore, we get
\[{\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}550000\]
We can find the gain using the formula \[{\text{Gain}} = {\text{S}}{\text{.P}}. - {\text{C}}{\text{.P}}{\text{.}}\].
Substituting \[{\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}550000\] and \[{\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}500000\] in the formula, we get
\[{\text{Gain}} = {\text{Rs}}{\text{. }}550000 - {\text{Rs}}{\text{. }}500000\]
Subtracting the terms, we get
\[{\text{Gain}} = {\text{Rs}}{\text{. }}50000\]
Therefore, the gain on the sale of the house is Rs. 50000.
Finally, we will find the gain percent on the sale of the house.
The gain percent is given by \[{\text{Gain Percent}} = \dfrac{{{\text{Gain}}}}{{{\text{C}}{\text{.P}}{\text{.}}}} \times 100\], where \[{\text{C}}{\text{.P}}{\text{.}}\] is the cost price of the object.
Substituting \[{\text{Gain}} = {\text{Rs}}{\text{. }}50000\] and \[{\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}500000\] in the formula, we get
\[{\text{Gain Percent}} = \dfrac{{50000}}{{500000}} \times 100\]
Simplifying the expression, we get
\[\begin{array}{l} \Rightarrow {\text{Gain Percent}} = \dfrac{{50000}}{{5000}}\\ \Rightarrow {\text{Gain Percent}} = 10\% \end{array}\]

\[\therefore\] The gain percent on the sale of the house is \[10\% \].

Note:
We must remember to include the cost of repairs in the cost price of the house. A common mistake we can make is to use \[{\text{Rs}}{\text{. }}365000\] as the cost price. This will result in the calculation of the incorrect gain, and hence, the incorrect gain percent. Gain percent is defined as the percentage gained by the seller after selling the object.