A field is 100 m long and 80 m wide . It has two cross roads at its centre of uniform width of 3 m such that one road is parallel to its length while the other is parallel to its breadth.Find the cost of gravelling the roads as Rs.5 per square metre.
Answers
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