A milkman purchases milk at Rs 30 per litre and added 6 litres of water. By selling the resultant mixture at Rs 30 per litre, he made a profit of 15%. How many litres of milk did he buy initially?

Let's solve the problem step by step.

### Given:
- Cost price (CP) of milk = Rs 30 per litre
- He adds 6 litres of water (which costs nothing)
- Selling price (SP) of the mixture = Rs 30 per litre
- Profit made = 15%

### To find:
The initial amount of milk purchased by the milkman.

### Solution:

1. **Let the quantity of milk be \( x \) litres**.
  
2. The total volume of the mixture = \( x \) litres (milk) + 6 litres (water) = \( x + 6 \) litres.
  
3. **Selling price (SP) of the entire mixture**:
   \[
   \text{SP} = (x + 6) \times 30 \text{ Rs}
   \]
   
4. **Cost price (CP) of the milk**:
   \[
   \text{CP} = x \times 30 \text{ Rs}
   \]
  
5. **According to the profit percentage**:
   \[
   \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right)
   \]
   Substituting the values:
   \[
   (x + 6) \times 30 = x \times 30 \times \left(1 + \frac{15}{100}\right)
   \]
   \[
   (x + 6) \times 30 = x \times 30 \times 1.15
   \]

6. Simplifying the equation:
   \[
   x + 6 = 1.15x
   \]
   \[
   1.15x - x = 6
   \]
   \[
   0.15x = 6
   \]
   \[
   x = \frac{6}{0.15} = 40
   \]

### Answer:
The milkman initially bought **40 litres** of milk.

Would you like more details or have any questions?

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Here are some related questions:

1. What would be the profit percentage if the selling price per litre was Rs 35 instead?
2. How much water would need to be added to achieve a 20% profit with the same selling price?
3. What would be the selling price per litre to achieve a 25% profit without adding any water?
4. If the milk was bought at Rs 35 per litre instead, how much water should be added to maintain the same 15% profit at Rs 30 per litre selling price?
5. What if the milkman sells the mixture for Rs 25 per litre? What would be the new profit or loss percentage?

**Tip:** When dealing with mixtures, remember that profit calculations are based on the cost price of the original substance, not the mixture itself.

Learn how to calculate the initial quantity of milk purchased by a milkman to achieve a 15% profit after adding water to the mixture. Step-by-step solution provided.

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