The cost of papering the walls of a room 12 m long at the rate of Rs. 13.50 per square metre is Rs. 3402 and the cost of matting the floor at Rs. 9.50 per square metre is Rs. 1026. Find the height of the room.

Answer

To find the height of the room given the costs of papering the walls and matting the floor, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Length of the room (L) = 12 m
- Cost of papering the walls = Rs. 3402
- Cost per square meter for papering = Rs. 13.50
- Cost of matting the floor = Rs. 1026
- Cost per square meter for matting = Rs. 9.50

2. **Calculate the Area of the Walls**:
- The total cost of papering the walls can be expressed as:
\[ \text{Area of walls} \times \text{Cost per square meter} = \text{Total cost} \]
- Let \( A \) be the area of the walls:
\[ A \times 13.50 = 3402 \]
- Solving for \( A \):
\[ A = \frac{3402}{13.50} = 252 \text{ m}^2 \]

3. **Set Up the Equation for the Area of the Walls**:
- The area of the four walls of the room can be calculated using the formula:
\[ \text{Area of four walls} = 2(LH + BH) \]
- Here, \( B \) is the breadth of the room, and \( H \) is the height of the room.
- Therefore:
\[ 2(12H + 9H) = 252 \]
- Simplifying gives:
\[ 2(21H) = 252 \]
- Dividing both sides by 2:
\[ 21H = 126 \]

4. **Calculate the Height of the Room**:
- Solving for \( H \):
\[ H = \frac{126}{21} = 6 \text{ m} \]

5. **Conclusion**:
- The height of the room is \( H = 6 \text{ m} \).