Let's break down the problem:

Given:

• The garden is 100 m long and 50 m wide.
• There is a road of 3 m wide around the garden.
• The cost of paving the road is Rs. 250 per square meter.

To Find:

The total cost of paving the road.

Approach:

1. Area of the garden (without the road):

   • Length = 100 m
   • Width = 50 m $\text{Area of garden} = \text{Length} \times \text{Width} = 100 \times 50 = 5000 \, \text{m}^2$

2. Area of the garden including the road:

   • Since the road is around the garden, the total dimensions increase by 3 m on each side.
   • New Length = $100 + 2 \times 3 = 106 \, \text{m}$
   • New Width = $50 + 2 \times 3 = 56 \, \text{m}$ $\text{Area of garden with road} = \text{New Length} \times \text{New Width} = 106 \times 56 = 5936 \, \text{m}^2$

3. Area of the road: The area of the road is the difference between the area of the garden with the road and the area of the garden without the road: $\text{Area of road} = \text{Area with road} - \text{Area of garden} = 5936 - 5000 = 936 \, \text{m}^2$

4. Cost of paving the road: The cost is given as Rs. 250 per square meter. $\text{Cost} = 936 \times 250 = 234000 \, \text{Rs}$

Answer:

The cost of paving the road is Rs. 234,000.

Would you like more details, or do you have any further questions?

Here are 5 related questions for practice:

1. If the cost per square meter increased to Rs. 300, what would be the new total cost?
2. How much area would the road cover if the garden was square, with a side length of 60 meters?
3. What would be the cost if the road was only 2 meters wide instead of 3 meters?
4. How would the area of the road change if the garden was 150 m long and 70 m wide?
5. How much would it cost to pave a circular road with a radius of 5 meters around a circular garden?

Tip: When calculating areas, always account for the increase in dimensions on both sides when something surrounds a given area.