A vendor buys bananas at 4 for Rs 3 and sells at 3 for Rs 4. What will be the result?

Options

A. 43.75% profit
B. 77.7% loss
C. 77.7% profit
D. 43.75% loss

Answer

To solve the problem step by step, we will first determine the cost price (CP) and selling price (SP) of one banana, then calculate the profit and profit percentage.

### Step 1: Calculate the Cost Price (CP) of one banana
The vendor buys 4 bananas for Rs 3.

To find the cost price of one banana, we can use the formula:
\[ \text{Cost Price of one banana} = \frac{\text{Total Cost}}{\text{Number of Bananas}} = \frac{3}{4} \text{ Rs} \]

### Step 2: Calculate the Selling Price (SP) of one banana
The vendor sells 3 bananas for Rs 4.

To find the selling price of one banana, we can use the formula:
\[ \text{Selling Price of one banana} = \frac{\text{Total Selling Price}}{\text{Number of Bananas}} = \frac{4}{3} \text{ Rs} \]

### Step 3: Calculate the Profit
Profit can be calculated using the formula:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Substituting the values we found:
\[ \text{Profit} = \frac{4}{3} - \frac{3}{4} \]

To perform this subtraction, we need a common denominator. The least common multiple of 3 and 4 is 12.

Converting both fractions:
\[ \frac{4}{3} = \frac{16}{12} \quad \text{and} \quad \frac{3}{4} = \frac{9}{12} \]

Now, substituting back into the profit formula:
\[ \text{Profit} = \frac{16}{12} - \frac{9}{12} = \frac{7}{12} \text{ Rs} \]

### Step 4: Calculate the Profit Percentage
Profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{\frac{7}{12}}{\frac{3}{4}}\right) \times 100 \]

To simplify \(\frac{7}{12} \div \frac{3}{4}\), we multiply by the reciprocal:
\[ \frac{7}{12} \times \frac{4}{3} = \frac{7 \times 4}{12 \times 3} = \frac{28}{36} = \frac{7}{9} \]

Now, substituting back into the profit percentage formula:
\[ \text{Profit Percentage} = \frac{7}{9} \times 100 \approx 77.78\% \]

### Final Result
The vendor makes a profit of approximately **77.78%**.

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