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This problem involves calculating the forces acting on a light horizontal rod, which is supported by two vertical strings at points \( A \) and \( B \). The rod is in equilibrium, meaning the sum of all forces and the sum of all moments (torques) must be zero.

### Given Information:
- Force at point \( C \) = 21 N (acting vertically downward)
- Force at point \( D \) = 25 N (acting vertically downward)
- Distance between \( A \) and \( C \) = 4 m
- Distance between \( C \) and \( D \) = 10 m
- Distance between \( D \) and \( B \) = 6 m
- Forces \( P \) and \( Q \) are the tensions in the strings at points \( A \) and \( B \), respectively, which act vertically upward.

### Conditions of Equilibrium:
1. **Vertical Force Balance**:
   \[
   P + Q = 21 + 25 = 46 \, \text{N}
   \]
   This ensures that the upward forces balance the downward forces.

2. **Moment Balance** (taking moments about point \( A \) to eliminate \( P \)):
   The moment due to \( P \) is zero, so we focus on the moments from the other forces about point \( A \).
   
   Moment equation:
   \[
   \text{Moment from } Q - \text{Moment from 21 N} - \text{Moment from 25 N} = 0
   \]
   \[
   Q \times (4 + 10 + 6) - 21 \times 4 - 25 \times (4 + 10) = 0
   \]
   \[
   Q \times 20 - 84 - 350 = 0
   \]
   \[
   Q \times 20 = 434
   \]
   \[
   Q = \frac{434}{20} = 21.7 \, \text{N}
   \]

3. **Finding \( P \)**:
   Using the force balance equation \( P + Q = 46 \):
   \[
   P + 21.7 = 46
   \]
   \[
   P = 46 - 21.7 = 24.3 \, \text{N}
   \]

### Final Answer:
- \( P = 24.3 \, \text{N} \)
- \( Q = 21.7 \, \text{N} \)

Would you like further details or clarification?

### Related Questions:
1. How would the forces change if the rod were not "light" and had a weight distributed along its length?
2. What would happen to the forces \( P \) and \( Q \) if the positions of the 21 N and 25 N forces were swapped?
3. How would the moments be calculated if the point of reference were point \( B \) instead of \( A \)?
4. How does the equilibrium condition change if the rod is tilted instead of being horizontal?
5. Can you calculate the tension in each string if the rod is subjected to an additional force at its midpoint?

**Tip:** When dealing with equilibrium problems, always remember that both the sum of forces and the sum of moments must be zero for equilibrium to be maintained.

The diagram shows a light rod held horizontally in equilibrium by two vertical strings. Find the magnitudes of the forces P and Q.

Solve the equilibrium problem of a light horizontal rod supported by two vertical strings, given forces acting downward at specific points. Includes force balance and moment balance conditions.

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