Step 1: Convert the depth of the gravel to meters. The depth of the gravel is given as $1 \text{ cm}$. Since $1 \text{ m} = 100 \text{ cm}$, we convert centimeters to meters: $$1 \text{ cm} = \frac{1}{100} \text{ m} = 0.01 \text{ m}$$ Step 2: Calculate the volume of gravel needed. The area of the courtyard is $3750 \text{ m}^2$. The volume of gravel is the area multiplied by the depth. $$\text{Volume} = \text{Area} \times \text{Depth}$$ $$\text{Volume} = 3750 \text{ m}^2 \times 0.01 \text{ m}$$ $$\text{Volume} = 37.5 \text{ m}^3$$ Step 3: Calculate the total cost of covering the courtyard with gravel. 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 $\boxed{₹240}$.