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The question asks:

"If \( P \) is 40% less than \( Q \), then \( Q \) is how much percentage more than \( P \)?"

### Step-by-Step Solution:

1. **Relationship Between \( P \) and \( Q \)**:
   If \( P \) is 40% less than \( Q \), then:
   \[
   P = Q - 0.4Q = 0.6Q
   \]
   So, \( P = 0.6Q \).

2. **How Much More is \( Q \) Than \( P \)?**
   We need to find by what percentage \( Q \) is greater than \( P \). The formula to find the percentage increase from \( P \) to \( Q \) is:
   \[
   \text{Percentage Increase} = \left( \frac{Q - P}{P} \right) \times 100
   \]

3. **Substitute the Value of \( P \)**:
   Since \( P = 0.6Q \), we substitute into the formula:
   \[
   \text{Percentage Increase} = \left( \frac{Q - 0.6Q}{0.6Q} \right) \times 100
   \]
   Simplify:
   \[
   \text{Percentage Increase} = \left( \frac{0.4Q}{0.6Q} \right) \times 100 = \frac{2}{3} \times 100 = 66.67\%
   \]

Thus, \( Q \) is **66.67%** more than \( P \).

Would you like more details, or do you have any questions?

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Here are 5 related questions:
1. If \( P \) were 50% less than \( Q \), what percentage more would \( Q \) be than \( P \)?
2. How would the percentage change if \( P \) were only 20% less than \( Q \)?
3. If \( Q \) is 60% more than \( P \), what percentage less is \( P \) than \( Q \)?
4. How can you generalize the percentage difference formula for any value of \( P \) and \( Q \)?
5. If \( P \) is 80% of \( Q \), how much percentage is \( Q \) more than \( P \)?

### Tip:
Always use the percentage change formula carefully, noting whether you're finding a percentage increase or decrease, depending on the comparison direction (from smaller to larger or vice versa).

If P is 40% less than Q, then Q is how much percentage more than P?

This page explains how to calculate the percentage increase of Q compared to P when P is 40% less than Q. Using the formula, students can learn how to solve algebraic percentage problems. Suitable for Grades 8-10.

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