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

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:

1. Unit Price Method: Calculate the CP and SP of a single item. This is often simple if the numbers are easy to divide.
2. 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.