Rohan purchased a table at the rate of Rs. 275 per table. If he sells 16 tables for Rs. 5060, then what will be the profit percentage?
15%
Understanding the Profit Percentage Problem
This problem involves calculating the profit percentage made by Rohan when selling tables. To find the profit percentage, we first need to determine the total cost price (CP) of the tables and the total selling price (SP) of the tables. The profit is the difference between the selling price and the cost price. The profit percentage is calculated relative to the cost price.
Calculating the Cost Price (CP)
Rohan purchased each table at the rate of Rs. 275. He purchased 16 tables. To find the total cost price for 16 tables, we multiply the cost per table by the number of tables.
Cost Price per table = Rs. 275
Number of tables purchased = 16
Total Cost Price (CP) for 16 tables = Cost Price per table $\times$ Number of tables
Total CP $= 275 \times 16$
Let's perform the calculation:
| Calculation | Value |
|---|---|
| $275 \times 10$ | $2750$ |
| $275 \times 6$ | $1650$ |
| $2750 + 1650$ | $4400$ |
So, the Total Cost Price (CP) for 16 tables is Rs. 4400.
Calculating the Selling Price (SP)
The problem states that Rohan sells 16 tables for Rs. 5060. This is the total selling price for the 16 tables.
Total Selling Price (SP) for 16 tables = Rs. 5060.
Calculating the Profit
Profit is the difference between the Selling Price (SP) and the Cost Price (CP).
Profit = SP - CP
Profit = Rs. 5060 - Rs. 4400
Profit = Rs. 660
Rohan made a profit of Rs. 660 on selling 16 tables.
Calculating the Profit Percentage
The profit percentage is calculated using the formula:
Profit Percentage $= \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100$
Using the values we calculated:
Profit = Rs. 660
Cost Price (CP) = Rs. 4400
Profit Percentage $= \left( \frac{660}{4400} \right) \times 100$
Simplify the fraction:
- $\frac{660}{4400}$ can be simplified by dividing both numerator and denominator by 10: $\frac{66}{440}$
- Both 66 and 440 are divisible by 2: $\frac{33}{220}$
- Both 33 and 220 are divisible by 11: $\frac{3}{20}$
So, the fraction is $\frac{3}{20}$.
Now, calculate the profit percentage:
Profit Percentage $= \frac{3}{20} \times 100$
Profit Percentage $= 3 \times \frac{100}{20}$
Profit Percentage $= 3 \times 5$
Profit Percentage $= 15\%$
The profit percentage is 15%.
Statement Analysis and Conclusion
Let's review the steps taken to calculate the profit percentage:
- Calculated the total cost price for 16 tables based on the per-table cost.
- Identified the total selling price for 16 tables.
- Calculated the absolute profit amount by subtracting the cost price from the selling price.
- Used the profit and the cost price to calculate the profit percentage.
The calculated profit percentage is 15%.
Revision Table: Profit Calculation
| Item | Value |
|---|---|
| Cost Price per Table | Rs. 275 |
| Number of Tables | 16 |
| Total Cost Price (CP) | $275 \times 16$ = Rs. 4400 |
| Total Selling Price (SP) | Rs. 5060 |
| Profit (SP - CP) | $5060 - 4400$ = Rs. 660 |
| Profit Percentage | $\left( \frac{660}{4400} \right) \times 100$ = 15% |
Additional Information on Profit and Loss Concepts
Understanding profit and loss is fundamental in commercial arithmetic. Here are some key terms and concepts:
- Cost Price (CP): The price at which an article is bought.
- Selling Price (SP): The price at which an article is sold.
- Profit: Occurs when SP > CP. Profit = SP - CP.
- Loss: Occurs when SP < CP. Loss = CP - SP.
- Profit Percentage: Calculated as $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$. Always calculated on the cost price unless otherwise stated.
- Loss Percentage: Calculated as $\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100$. Always calculated on the cost price unless otherwise stated.
- The terms 'gain' and 'profit' are often used interchangeably.
These concepts help in analyzing the profitability of transactions.
Important Questions from Successive Selling
the cost price of an article is 30% less than the selling price of that article, then what will be the profit percentage?
A single discount equivalent to three successive discounts i.e. 7%, 12% and 5% is:
Two successive discounts, with the first being 10%, were given on an article having the marked price of ₹ 7,500. Finally, it was sold for ₹ 5,805. What percent was the second discount ?
The marked price of an article is ₹450. It is sold for ₹267.30, after offering three successive discounts of 10%, x%, and 20%. What is the value of x?
A Shopkeeper loses 10% on selling an article for Rs. 360. To gain 30%, what should have been selling price of the article?
