The cost of 50 dozens of bananas is Rs. 2,400 and the transport cost per banana is Rs. 0.25. The selling price is Rs. 10 for a pair of bananas. What is the profit percentage (rounded off up to one decimal place)?
17.6%
Calculating Profit Percentage on Bananas
This problem requires us to calculate the profit percentage earned from buying and selling bananas. We are given the purchase cost for a large quantity, the transport cost per individual banana, and the selling price per pair of bananas. To find the profit percentage, we need to determine the total cost price (including transport) and the total selling price, then use the formula for profit percentage.
Step 1: Determine the Total Number of Bananas
We are given the cost of 50 dozens of bananas. One dozen contains 12 bananas.
Total number of bananas = Number of dozens \(\times\) Bananas per dozen
\( \text{Total bananas} = 50 \times 12 = 600 \text{ bananas} \)
Step 2: Calculate the Total Cost Price (CP)
The total cost price includes the initial purchase cost and the transport cost for all the bananas.
- Initial purchase cost = Rs. 2,400
- Transport cost per banana = Rs. 0.25
Total transport cost = Total number of bananas \(\times\) Transport cost per banana
\( \text{Total transport cost} = 600 \times 0.25 \)
\( \text{Total transport cost} = 600 \times \frac{1}{4} = 150 \text{ Rupees} \)
Total Cost Price (CP) = Initial purchase cost + Total transport cost
\( \text{CP} = 2400 + 150 = 2550 \text{ Rupees} \)
Step 3: Calculate the Total Selling Price (SP)
The bananas are sold in pairs, and the selling price for a pair is Rs. 10. First, we need to find out how many pairs can be made from the total number of bananas.
Number of pairs = Total number of bananas \(\div\) Bananas per pair
\( \text{Number of pairs} = 600 \div 2 = 300 \text{ pairs} \)
Total Selling Price (SP) = Number of pairs \(\times\) Selling price per pair
\( \text{SP} = 300 \times 10 = 3000 \text{ Rupees} \)
Step 4: Calculate the Profit
Profit is the difference between the Total Selling Price and the Total Cost Price.
Profit = SP - CP
\( \text{Profit} = 3000 - 2550 = 450 \text{ Rupees} \)
Step 5: Calculate the Profit Percentage
The profit percentage is calculated with respect to the Cost Price. The formula is:
\( \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \)
\( \text{Profit Percentage} = \left( \frac{450}{2550} \right) \times 100 \)
We can simplify the fraction:
\( \frac{450}{2550} = \frac{45}{255} = \frac{9 \times 5}{51 \times 5} = \frac{9}{51} = \frac{3 \times 3}{17 \times 3} = \frac{3}{17} \)
Now calculate the percentage:
\( \text{Profit Percentage} = \left( \frac{3}{17} \right) \times 100 = \frac{300}{17} \)
Let's perform the division:
\( 300 \div 17 \approx 17.647... \)
Rounding the profit percentage to one decimal place gives us 17.6%.
Therefore, the profit percentage is approximately 17.6%.
Revision Table: Banana Cost and Profit
| Item | Calculation/Value |
|---|---|
| Total Bananas | \( 50 \text{ dozen} \times 12 \text{ bananas/dozen} = 600 \text{ bananas} \) |
| Initial Purchase Cost | Rs. 2,400 |
| Total Transport Cost | \( 600 \text{ bananas} \times \text{Rs. } 0.25/\text{banana} = \text{Rs. } 150 \) |
| Total Cost Price (CP) | \( \text{Rs. } 2400 + \text{Rs. } 150 = \text{Rs. } 2550 \) |
| Number of Pairs | \( 600 \text{ bananas} \div 2 \text{ bananas/pair} = 300 \text{ pairs} \) |
| Total Selling Price (SP) | \( 300 \text{ pairs} \times \text{Rs. } 10/\text{pair} = \text{Rs. } 3000 \) |
| Profit | \( \text{Rs. } 3000 - \text{Rs. } 2550 = \text{Rs. } 450 \) |
| Profit Percentage | \( \left( \frac{\text{Rs. } 450}{\text{Rs. } 2550} \right) \times 100 \approx 17.6\% \) |
Additional Information on Profit Calculation
Understanding cost price, selling price, profit, and profit percentage is fundamental in business and mathematics. Here are some key concepts related to this problem:
- Cost Price (CP): The total expense incurred to acquire a product or service. This can include purchase cost, transport, handling charges, etc., as seen in the banana problem.
- Selling Price (SP): The price at which a product or service is sold to the customer.
- Profit: Occurs when the Selling Price is greater than the Cost Price (SP > CP). Profit = SP - CP.
- Loss: Occurs when the Selling Price is less than the Cost Price (SP < CP). Loss = CP - SP.
- Profit Percentage: Calculated as the profit relative to the cost price, expressed as a percentage. The formula is always \(\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\).
- Loss Percentage: Calculated as the loss relative to the cost price, expressed as a percentage. The formula is \(\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\).
It's important to correctly identify all components that contribute to the cost price before calculating profit or loss percentages.
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