Hemant buys a dozen eggs for Rs. 5.50 per egg. While carrying them, two eggs wasted when fall down and get damaged. He sells the balanced eggs at Rs. 7.70 per egg. Find the net profit earned by him in the overall deal.
Rs. 11.00
Understanding the Profit and Loss Problem
This problem involves calculating the net profit made by Hemant from buying, losing some, and selling eggs. We need to first find the total cost incurred and the total revenue generated from the sale of the remaining eggs. The difference between the total selling price and the total cost price will give us the net profit.
Calculating the Total Cost Price
Hemant bought a dozen eggs. A dozen means 12 items. The cost per egg was given as Rs. 5.50.
To find the total cost price (CP), we multiply the number of eggs bought by the cost per egg.
Number of eggs bought = 1 dozen = 12 eggs
Cost per egg = Rs. 5.50
Total Cost Price (CP) = Number of eggs bought × Cost per egg
Total CP $= 12 \times 5.50$
Let's perform the multiplication:
- $12 \times 5 = 60$
- $12 \times 0.50 = 6.00$
- $60 + 6.00 = 66.00$
Total Cost Price = Rs. 66.00
Calculating the Total Selling Price
Out of the 12 eggs bought, 2 eggs were wasted and damaged. This means Hemant could only sell the remaining eggs.
Number of eggs wasted = 2 eggs
Number of eggs sold = Total eggs bought - Number of eggs wasted
Number of eggs sold $= 12 - 2 = 10$ eggs
The selling price per egg was given as Rs. 7.70.
To find the total selling price (SP), we multiply the number of eggs sold by the selling price per egg.
Number of eggs sold = 10 eggs
Selling price per egg = Rs. 7.70
Total Selling Price (SP) = Number of eggs sold × Selling price per egg
Total SP $= 10 \times 7.70$
Multiplying by 10 is straightforward, we just move the decimal point one place to the right.
Total Selling Price = Rs. 77.00
Calculating the Net Profit
Profit is calculated when the total selling price is greater than the total cost price. The net profit is the difference between the total selling price and the total cost price.
Net Profit = Total Selling Price (SP) - Total Cost Price (CP)
Net Profit $= 77.00 - 66.00$
Net Profit $= 11.00$
The net profit earned by Hemant in the overall deal is Rs. 11.00.
Summary of Calculations
| Item | Quantity | Price per Item | Total Price |
|---|---|---|---|
| Eggs Bought (Cost) | 12 | Rs. 5.50 | $12 \times 5.50 = \text{Rs. } 66.00$ (CP) |
| Eggs Wasted | 2 | - | - |
| Eggs Sold (Revenue) | 10 | Rs. 7.70 | $10 \times 7.70 = \text{Rs. } 77.00$ (SP) |
Net Profit = Total SP - Total CP
Net Profit = Rs. 77.00 - Rs. 66.00
Net Profit = Rs. 11.00
Conclusion on Net Profit
Based on the calculations, Hemant made a net profit of Rs. 11.00 from the deal.
Revision Table: Profit & Loss Concepts
| Concept | Definition | Formula |
|---|---|---|
| Cost Price (CP) | The price at which an item is bought. | - |
| Selling Price (SP) | The price at which an item is sold. | - |
| Profit | Occurs when SP > CP. | Profit = SP - CP |
| Loss | Occurs when CP > SP. | Loss = CP - SP |
| Net Profit/Loss | Total SP from all units sold minus Total CP for all units bought (considering any units lost or damaged). | Net Profit = Total SP - Total CP |
Additional Information on Profit Calculation
When calculating profit or loss, it's important to consider all factors that affect the total cost and the total revenue. In this problem, the damaged eggs reduced the number of items that could be sold, directly impacting the total selling price. The initial cost, however, was for the total number of eggs purchased, regardless of whether they were sold or not.
Profit percentage can also be calculated based on the cost price: $\text{Profit \%} = \frac{\text{Net Profit}}{\text{Total CP}} \times 100$. In this case, $\text{Profit \%} = \frac{11}{66} \times 100 = \frac{1}{6} \times 100 \approx 16.67\%$.
This type of problem is common in basic arithmetic and business calculations to understand profitability.
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