A vendor buys bananas at 9 for Rs 8 and sells at 8 for Rs 9. What will be the profit or loss (in%) ?

Options

A. 13.28% profit
B. 26.56% loss
C. 26.56% profit
D. 13.28% loss

Answer

To solve the problem step by step, we need to find the cost price (CP) and selling price (SP) of the bananas, and then calculate the profit or loss percentage.

### Step 1: Calculate the Cost Price (CP)
The vendor buys bananas at 9 for Rs 8.
- Therefore, the cost price for 9 bananas = Rs 8.
- To find the cost price per banana, we divide the total cost by the number of bananas:

\[ \text{CP per banana} = \frac{8}{9} \text{ Rs} \]

### Step 2: Calculate the Selling Price (SP)
The vendor sells bananas at 8 for Rs 9.
- Therefore, the selling price for 8 bananas = Rs 9.
- To find the selling price per banana, we divide the total selling price by the number of bananas:

\[ \text{SP per banana} = \frac{9}{8} \text{ Rs} \]

### Step 3: Calculate the Profit or Loss
Now, we need to find the profit or loss per banana by subtracting the cost price from the selling price:

\[ \text{Profit per banana} = \text{SP} - \text{CP} = \frac{9}{8} - \frac{8}{9} \]

To perform the subtraction, we need a common denominator. The least common multiple of 8 and 9 is 72.

- Convert \(\frac{9}{8}\) to a fraction with a denominator of 72:

\[ \frac{9}{8} = \frac{9 \times 9}{8 \times 9} = \frac{81}{72} \]

- Convert \(\frac{8}{9}\) to a fraction with a denominator of 72:

\[ \frac{8}{9} = \frac{8 \times 8}{9 \times 8} = \frac{64}{72} \]

Now we can subtract:

\[ \text{Profit per banana} = \frac{81}{72} - \frac{64}{72} = \frac{17}{72} \text{ Rs} \]

### Step 4: Calculate the Profit Percentage
To find the profit percentage, we use the formula:

\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Profit Percentage} = \left( \frac{\frac{17}{72}}{\frac{8}{9}} \right) \times 100 \]

First, we simplify the fraction:

\[ \frac{\frac{17}{72}}{\frac{8}{9}} = \frac{17}{72} \times \frac{9}{8} = \frac{17 \times 9}{72 \times 8} = \frac{153}{576} \]

Now, we can calculate the profit percentage:

\[ \text{Profit Percentage} = \frac{153}{576} \times 100 \approx 26.56\% \]

### Conclusion
The vendor makes a profit of approximately **26.56%**.

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