Find the area of the iron sheet required to make the cistern. If it is hammered into a sheet to cover an area of 12 m².

The depth of the gravel is given as $1 \text{ cm}$.
Since $1 \text{ m} = 100 \text{ cm}$, we convert centimeters to meters:

$$1 \text{ cm} = \frac{1}{100} \text{ m} = 0.01 \text{ m}$$

The area of the courtyard is $3750 \text{ m}^2$.
The volume of gravel is the area multiplied by the depth.

$$\text{Volume} = \text{Area} \times \text{Depth}$$ $$\text{Volume} = 3750 \text{ m}^2 \times 0.01 \text{ m}$$ $$\text{Volume} = 37.5 \text{ m}^3$$

The cost of gravel is ₹6.40 per cubic meter.

$$\text{Total Cost} = \text{Volume} \times \text{Cost per cubic meter}$$ $$\text{Total Cost} = 37.5 \text{ m}^3 \times ₹6.40/\text{m}^3$$ $$\text{Total Cost} = ₹240$$

The cost of covering the courtyard with gravel is $₹240$.