The madhu and kavitha purchased a new house question is a profit and loss problem from Class 8 Mathematics, Chapter 5, Comparing Quantities Using Proportion. It asks you to calculate the financial loss and loss percentage when a house is sold for less than its original purchase price.
Madhu and Kavitha purchased a house for ₹3,20,000. However, due to economic problems, they had to sell it for ₹2,80,000. The question requires you to find the total loss incurred and the percentage of loss on the transaction.
Quick Answer:
- Total loss: ₹40,000
- Loss percentage: 12.5%
Understanding the Madhu and Kavitha Purchased a New House Question
The problem presents a real-life situation involving the purchase and sale of a property. Madhu and Kavitha initially buy a house for ₹3,20,000. Later, because of financial difficulties, they decide to sell it for ₹2,80,000.
You need to find the difference between the purchase price and selling price. This difference represents the loss. After calculating the amount, you must express it as a percentage of the original cost price.
Here is the information provided in the question:
| Particulars | Amount |
| Cost Price (CP) | ₹3,20,000 |
| Selling Price (SP) | ₹2,80,000 |
| Reason for selling | Economic problems |
| Required calculation | Loss and loss percentage |
The two important terms you should understand before solving this problem are:
- Cost Price (CP): The original amount paid to purchase the house. In this example, it is ₹3,20,000.
- Selling Price (SP): The amount received after selling the house. Here, it is ₹2,80,000.
Since the selling price is lower than the cost price, Madhu and Kavitha have incurred a loss.
Step-by-Step Solution of the Madhu and Kavitha House Question
To solve this Class 8 Maths profit and loss problem, you need two formulas. The first helps you calculate the actual loss, while the second converts that amount into a percentage.
Step 1: Identify Whether It Is a Profit or Loss
The first step is to compare the cost price with the selling price.
- Cost Price = ₹3,20,000
- Selling Price = ₹2,80,000
You can identify the result using a simple rule:
- When Selling Price is greater than Cost Price, there is a profit.
- When Selling Price is less than Cost Price, there is a loss.
- When both prices are equal, there is neither profit nor loss.
In this question, the selling price of ₹2,80,000 is lower than the purchase price of ₹3,20,000. Therefore, Madhu and Kavitha incurred a loss when they sold their house.
Step 2: Calculate the Total Loss
Once you identify the transaction as a loss, subtract the selling price from the cost price.
Formula:
Loss = Cost Price − Selling Price
Now, substitute the given values:
Loss = ₹3,20,000 − ₹2,80,000
Loss = ₹40,000
Total Loss = ₹40,000
Therefore, Madhu and Kavitha lost ₹40,000 on the sale of their house.
Step 3: Calculate the Loss Percentage
Finding the total loss is only the first part of the question. You also need to calculate the loss percentage to understand how much they lost compared with the original purchase price.
For this calculation, use the following formula:
Formula:
Loss Percentage = (Loss ÷ Cost Price) × 100
We already know:
- Loss = ₹40,000
- Cost Price = ₹3,20,000
Substitute these values:
= (₹40,000 ÷ ₹3,20,000) × 100
= 0.125 × 100
= 12.5%
Loss Percentage = 12.5%
Hence, Madhu and Kavitha incurred a loss of 12.5% on the original purchase price of their house.
Final Answer to the Madhu and Kavitha House Problem
After applying the profit and loss formulas, you get the following answers:
| Question | Answer |
| Total loss incurred | ₹40,000 |
| Loss percentage | 12.5% |
Final result: Madhu and Kavitha incurred a total loss of ₹40,000, which represents 12.5% of the cost price.
These are the two values required to complete the textbook exercise.
Important Profit and Loss Formulas for Class 8
The Comparing Quantities Using Proportion chapter covers several mathematical concepts, including ratios, percentages, profit and loss. Learning the basic formulas makes it easier to solve different word problems.
Here are the important profit and loss formulas you should remember:
| Concept | Formula |
| Profit | Selling Price − Cost Price |
| Loss | Cost Price − Selling Price |
| Profit Percentage | (Profit ÷ Cost Price) × 100 |
| Loss Percentage | (Loss ÷ Cost Price) × 100 |
Understanding the formulas:
- Profit: The extra amount earned when you sell an item for more than its purchase price.
- Loss: The amount you lose when you sell something for less than its original cost.
- Profit Percentage: The profit expressed as a percentage of the cost price.
- Loss Percentage: The loss expressed as a percentage of the cost price.
One important point to remember is that both profit percentage and loss percentage are calculated using the cost price as the base value.
For example, in the house problem, the loss is ₹40,000. To find its percentage, you divide this amount by ₹3,20,000 rather than ₹2,80,000.
Common Mistakes to Avoid While Solving This Question
Even simple profit and loss questions can become confusing when you use the wrong formula or calculation method. Keep the following points in mind while solving similar Class 8 Mathematics problems.
- Subtracting the prices in the wrong order: For a loss, always subtract the selling price from the cost price. Reversing the values can give you an incorrect result.
- Using the selling price to calculate loss percentage: The cost price is always used as the base when calculating loss percentage. Do not divide the loss by the selling price.
- Forgetting to multiply by 100: Dividing the loss by the cost price gives you a decimal value. Multiply it by 100 to convert it into a percentage.
- Confusing the loss amount with the loss percentage: ₹40,000 is the actual amount lost, whereas 12.5% represents that loss in percentage form.
- Skipping calculation steps: Writing the formula, substituting the values and showing the final result makes your answer easier to understand and check.
Following these simple points will help you solve profit and loss word problems more accurately in your school examinations.
Wrapping Up
The madhu and kavitha purchased a new house problem is a straightforward example of how you can apply profit and loss formulas to a real-life situation. The house was originally purchased for ₹3,20,000 and later sold for ₹2,80,000 due to economic problems.
The difference between these two amounts gives a total loss of ₹40,000. When you calculate this loss as a percentage of the original cost price, the result is 12.5%.
Remember that the cost price is the base value for calculating both profit and loss percentages. Understanding this rule will help you solve similar questions from Class 8 Maths and prepare more confidently for your examinations.
