A water tank is 15 meter long, 10 meter wide and 3 meter deep. The total cost to repair its four walls and bottom at the rate of 24 rupees per square meter is :

Question

Accepted Answer

To determine the total cost to repair the four walls and the bottom of the water tank, we need to calculate the total surface area that requires repair and then multiply it by the cost per square meter.

### Step-by-Step Calculation:

1. **Dimensions of the Tank:**
   - Length (L) = 15 meters
   - Width (W) = 10 meters
   - Depth (H) = 3 meters

2. **Surface Area Calculation:**
   - **Bottom Area:** The bottom of the tank is a rectangle with dimensions 15 meters by 10 meters.
     $$
     \text{Bottom Area} = L \times W = 15 \times 10 = 150 \text{ square meters}
     $$

- **Wall Areas:** The tank has four walls. Two pairs of opposite walls have different dimensions:
     - **Two longer walls:** Each has dimensions 15 meters by 3 meters.
       $$
       \text{Area of two longer walls} = 2 \times (L \times H) = 2 \times (15 \times 3) = 90 \text{ square meters}
       $$
     - **Two shorter walls:** Each has dimensions 10 meters by 3 meters.
       $$
       \text{Area of two shorter walls} = 2 \times (W \times H) = 2 \times (10 \times 3) = 60 \text{ square meters}
       $$

- **Total Wall Area:**
     $$
     \text{Total Wall Area} = 90 + 60 = 150 \text{ square meters}
     $$

3. **Total Surface Area to be Repaired:**
   - The total area that needs repair is the sum of the bottom area and the wall areas.
     $$
     \text{Total Surface Area} = \text{Bottom Area} + \text{Total Wall Area} = 150 + 150 = 300 \text{ square meters}
     $$

4. **Cost Calculation:**
   - The cost to repair is given at 24 rupees per square meter.
     $$
     \text{Total Cost} = \text{Total Surface Area} \times \text{Cost per square meter} = 300 \times 24 = 7200 \text{ rupees}
     $$

### Conclusion:

- **Correct Option:** The total cost to repair the four walls and the bottom of the tank is 7200 rupees, which corresponds to **Option 4**.

### Explanation of Incorrect Options:

- **Option 1 (Rs. 9600):** This option suggests a higher cost, which would imply a larger surface area or a higher rate per square meter, neither of which is correct based on the given dimensions and rate.
  
- **Option 2 (Rs. 4800):** This option suggests a lower cost, which would imply a smaller surface area or a lower rate per square meter, neither of which matches the given problem.

- **Option 3 (Rs. 3600):** This option also suggests a significantly lower cost, which does not align with the calculated total surface area and rate.

Thus, the correct answer, supported by the calculations, is **Option 4: Rs. 7200**.