Vikash purchased 5 bananas for Rs. 4 and sold 4 bananas for Rs. 5. Calculate his % profit? A. 55.56% B. 53.25% C. 45.50% D. 56.25%
D
Calculating Profit Percentage on Banana Sale
This problem involves calculating the profit percentage when the number of items bought and sold are different. To correctly determine the profit or loss, we need to find the cost price (CP) and selling price (SP) for the same number of items.
Let's analyze the given information:
- Vikash purchased 5 bananas for Rs. 4.
- Vikash sold 4 bananas for Rs. 5.
To compare the cost and selling prices, we can find the price for a common number of bananas. The least common multiple (LCM) of 5 and 4 is 20. Let's calculate the CP and SP for 20 bananas.
Calculating the Cost Price (CP)
The cost of 5 bananas is Rs. 4.
The cost of 1 banana is \(\text{Rs. } \frac{4}{5}\).
The cost of 20 bananas is \(\text{Rs. } \frac{4}{5} \times 20\).
Calculation:
\(\frac{4}{5} \times 20 = 4 \times \frac{20}{5} = 4 \times 4 = 16\)
So, the Cost Price (CP) of 20 bananas is Rs. 16.
Calculating the Selling Price (SP)
The selling price of 4 bananas is Rs. 5.
The selling price of 1 banana is \(\text{Rs. } \frac{5}{4}\).
The selling price of 20 bananas is \(\text{Rs. } \frac{5}{4} \times 20\).
Calculation:
\(\frac{5}{4} \times 20 = 5 \times \frac{20}{4} = 5 \times 5 = 25\)
So, the Selling Price (SP) of 20 bananas is Rs. 25.
Calculating the Profit
Profit is calculated as Selling Price (SP) minus Cost Price (CP).
Profit = SP - CP
Profit = Rs. 25 - Rs. 16
Profit = Rs. 9
Since the SP (Rs. 25) is greater than the CP (Rs. 16), Vikash made a profit.
Calculating the Profit Percentage
The profit percentage is calculated using the formula:
\(\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\%\)
Substituting the values:
\(\text{Profit Percentage} = \left( \frac{9}{16} \right) \times 100\%\)
Calculation:
\(\frac{9}{16} \times 100 = \frac{900}{16}\)
\(\frac{900}{16} = 56.25\)
So, the profit percentage is 56.25%.
Therefore, Vikash's profit percentage is 56.25%.
Let's compare this with the given options:
- A. 55.56%
- B. 53.25%
- C. 45.50%
- D. 56.25%
The calculated profit percentage matches option D.
Revision Table: Key Formulas
| Concept | Formula |
|---|---|
| Profit | SP - CP (when SP > CP) |
| Loss | CP - SP (when CP > SP) |
| Profit Percentage | \(\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\%\) |
| Loss Percentage | \(\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\%\) |
Additional Information: Handling Different Quantities in Profit and Loss Problems
When the number of items bought and sold is different, it's crucial to find the cost price (CP) and selling price (SP) for the same number of items before calculating profit or loss. There are two common methods:
- Unit Price Method: Calculate the CP and SP of a single item. This is often simple if the numbers are easy to divide.
- LCM Method: Find the least common multiple (LCM) of the number of items bought and the number of items sold. Calculate the CP and SP for this LCM quantity. This method avoids fractions in intermediate steps, which can be helpful.
In this problem, we used the LCM method by calculating the CP and SP for 20 bananas.
Understanding how to standardize the quantity is key to solving such profit and loss problems accurately.
Important Questions from Successive Selling
By selling a watch at Rs. 840 a person loses 4%. Find the gain or loss if he sold it for Rs. 875?
Gaurav bought some articles at 5 for Rs. 6 and sold them at 10 for Rs. 11. His loss percentage is:
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
- The selling price of 24 articles is equal to the cost price of 26 articles. If, due to a change in market conditions, the selling price of each article decreases by $10\%$ and the cost price of each article increases by $5\%$, what will be the new gain or loss percentage (correct to two decimal places)?
X sells goods to Y at a profit of 20 percent and Y sells the same goods to Z at a profit of 50 percent. If the cost price for Z is Rs 9000, then what is the cost of the goods for X?
