A fruit seller bought 600 bananas at 6 for Rs. 5 and sold at 5 for Rs. 5. Find:
(i) the cost price of all bananas.
(ii) the selling price of all bananas.
(iii) his profit and profit percentage on the whole deal.

Answer

Let's solve the problem step by step.

### Step 1: Calculate the Cost Price of All Bananas
The fruit seller bought 600 bananas at the rate of 6 bananas for Rs. 5.

To find the cost price of all bananas, we first determine how many groups of 6 bananas are in 600 bananas:
\[ \text{Number of groups} = \frac{600 \text{ bananas}}{6 \text{ bananas/group}} = 100 \text{ groups} \]

Now, we calculate the total cost price:
\[ \text{Cost Price} = \text{Number of groups} \times \text{Cost per group} = 100 \text{ groups} \times 5 \text{ Rs/group} = 500 \text{ Rs} \]

### Step 2: Calculate the Selling Price of All Bananas
The fruit seller sold the bananas at the rate of 5 bananas for Rs. 5.

To find the selling price of all bananas, we first determine how many groups of 5 bananas are in 600 bananas:
\[ \text{Number of groups} = \frac{600 \text{ bananas}}{5 \text{ bananas/group}} = 120 \text{ groups} \]

Now, we calculate the total selling price:
\[ \text{Selling Price} = \text{Number of groups} \times \text{Selling price per group} = 120 \text{ groups} \times 5 \text{ Rs/group} = 600 \text{ Rs} \]

### Step 3: Calculate Profit
Profit is calculated by subtracting the cost price from the selling price:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 600 \text{ Rs} - 500 \text{ Rs} = 100 \text{ Rs} \]

### Step 4: Calculate Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{100 \text{ Rs}}{500 \text{ Rs}}\right) \times 100 = 20\% \]

### Final Answers:
(i) The cost price of all bananas is Rs. 500.
(ii) The selling price of all bananas is Rs. 600.
(iii) The profit is Rs. 100 and the profit percentage is 20%.

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