A rectangular lawn 80 meters by 60 meters has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at Rs. 30 per square meter?

Explanation

Find the area of the rectangular lawn:

Area = Length x Breadth = 80m x 60m = 4800 square meters

Since there are two roads, one parallel to the length and one parallel to the breadth, we need to find the area of each road:

Road parallel to length:

Area = Length x Width = 80m x 10m = 800 square meters

Road parallel to breadth:

Area = Breadth x Width = 60m x 10m = 600 square meters

However, the problem states that the roads are running in the middle of the lawn, which means they intersect. To avoid double-counting the intersection area, we need to subtract it:

Intersection Area = Width x Width = 10m x 10m = 100 square meters

Now, add the areas of both roads and subtract the intersection area:

Total Road Area = (800 + 600) - 100 = 1300 square meters

Finally, calculate the cost of gravelling the roads at Rs. 30 per square meter:

Cost = Total Road Area x Rate = 1300 x 30 = Rs. 39000

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