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The problem involves determining the ratio \( x \) of paint Q when mixed with paint P, given that:

- The cost per liter of paint P is Ksh 220.
- The cost per liter of paint Q is Ksh 250.
- Paints P and Q are mixed in the ratio \( P : Q = 3 : x \).
- The mixture is sold at Ksh 300 per liter, with a profit of 25%.

### Step-by-Step Solution:

1. **Cost Price Calculation**:  
   Let the total cost price per liter of the mixture be denoted by \( C_{mixture} \).

   Since the paints are mixed in the ratio \( P : Q = 3 : x \), the quantities of paints P and Q in the mixture are \( 3 \) parts of P and \( x \) parts of Q.

   The cost price for 3 parts of P and \( x \) parts of Q is:
   \[
   C_{mixture} = \frac{3 \times 220 + x \times 250}{3 + x}
   \]

2. **Selling Price and Profit**:  
   The selling price of the mixture per liter is Ksh 300, and it includes a 25% profit. Therefore, the cost price per liter can be calculated as:
   \[
   C_{mixture} = \frac{300}{1 + 0.25} = \frac{300}{1.25} = 240 \, \text{Ksh}
   \]

   So, the total cost price per liter of the mixture is Ksh 240.

3. **Equating the Cost Prices**:
   Now, we can set up the equation by equating the cost price derived from the mixture and the cost price from the profit:
   \[
   \frac{3 \times 220 + x \times 250}{3 + x} = 240
   \]

4. **Solving for \( x \)**:
   Multiply both sides by \( 3 + x \):
   \[
   3 \times 220 + x \times 250 = 240 \times (3 + x)
   \]

   Simplify:
   \[
   660 + 250x = 720 + 240x
   \]

   Subtract \( 240x \) from both sides:
   \[
   660 + 10x = 720
   \]

   Subtract 660 from both sides:
   \[
   10x = 60
   \]

   Solve for \( x \):
   \[
   x = \frac{60}{10} = 6
   \]

### Final Answer:
The value of \( x \) is **6**.

---

Would you like further details or clarifications?

Here are five related questions you might find interesting:
1. How does changing the ratio of P to Q affect the final price?
2. What would be the selling price if the profit margin were 30% instead of 25%?
3. How can we calculate the cost price if we know the selling price and profit percentage?
4. How would the calculation change if the cost per liter of P and Q were swapped?
5. How do different ratios of mixtures impact the overall profit?

**Tip**: When dealing with mixture problems, always express the cost or quantities in terms of parts (ratios), and carefully set up equations based on profit or cost changes.

The cost of two types of paints, P and Q are Ksh 220 and Ksh 250 per litre respectively. The paints P and Q were mixed in the ratio P : Q = 3 : x and one litre of the mixture sold at Ksh 300, thereby making a profit of 25%. Determine the value of x.

Learn how to determine the ratio of paints P and Q mixed in a specific proportion to achieve a 25% profit. This problem involves key concepts in ratios, algebra, and profit calculation. Suitable for students in Grades 10-12.

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