Question

a field is 100m long and 80m wide. it has two cross roads at its centre of uniform width of its centre of uniform width of 3m such that one road is parallel to its breadth. find the cost of gravelling the roads as rs 5 per square metre.​

Answer 1

The cost of gravelling the roads at the rate of Rs. 5 per square metre is Rs. 2655.

Step-by-step explanation:

The length of the field = 100 m

The width of the field = 80 m

It is given that two crossroads of 3 m width are built in such a way that 1 road is parallel to the length of the field and the other is parallel to the width of the field.

Step (1): Road which is parallel to the length of the field

Here,

The length of the road will be = 100 m

The width of the road will be = 3 m

∴ Area of the road which is parallel to the length of the field = 100 * 3 = 300 m²

Step (2): Road which is parallel to the width of the field  

Here,

The length of the road will be = 80 m

The width of the road will be = 3 m

∴ Area of the road which is parallel to the width of the field = 80 * 3 = 240 m²

Step (3): The middle part of the road which is common between both the crossroads

Here,

Length = 3 m

Width = 3 m

∴ Area of the middle part of the road which is common between both the crossroads = 3 * 3 = 9 m²

Step (4):

Now,

The total area of crossroads for gravelling is given by,

= [Area of the road which is parallel to the length of the field] + [Area of the road which is parallel to the width of the field] – [Area of the middle part of the road which is common between both the crossroads]

= 300 + 240 – 9

= 531 m²

The cost of gravelling the roads is given as Rs. 5 per square metre.

Thus,  

The cost of gravelling the total area of crossroads will be,

= 531 m² * Rs. 5

= Rs. 2655

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