A residential society plans to renovate a rectangular community park measuring 60 metres in length and 40 metres in width. A walking track of uniform width 5 metres is constructed inside the park along all four boundaries. The remaining central portion is used for recreational activities. In one corner of this central area, a square flower garden of side 10 metres is developed. The society also decides to fence the entire outer boundary of the park at a cost of ₹150 per metre.
For maintenance purposes, the walking track will be covered with special paving tiles costing ₹200 per square metre. The remaining recreational area, excluding the flower garden, will be covered with grass. The management wants to calculate the total area occupied by different sections of the park and estimate the expenses involved in fencing and paving.
The renovation committee is required to determine the perimeter and area of the complete park, the area occupied by the walking track, the area available for recreation and the costs associated with different renovation activities.
Question 1
What is the perimeter of the entire rectangular park?
A. 180 metres
B. 190 metres
C. 240 metres
D. 200 metres
Question 2
What is the total cost of fencing the outer boundary of the park?
A. ₹25,000
B. ₹28,000
C. ₹32,000
D. ₹30,000
Question 3
What is the area of the walking track constructed inside the park?
A. 900 sq. metres
B. 1,000 sq. metres
C. 800 sq. metres
D. 1,100 sq. metres
Question 4
What is the area available for recreational activities after excluding both the walking track and the square flower garden?
A. 1,500 sq. metres
B. 1,300 sq. metres
C. 1,400 sq. metres
D. 1,600 sq. metres
Question 5
What is the total cost of paving the walking track?
A. ₹1,60,000
B. ₹1,80,000
C. ₹2,00,000
D. ₹1,50,000
Answers and Detailed Explanations
1. Correct Answer: D. 200 metres
The park is rectangular.
Perimeter of a rectangle:
Perimeter = 2 × (Length + Width)
Given:
Length = 60 metres
Width = 40 metres
Therefore,
Perimeter = 2 × (60 + 40)
= 2 × 100
= 200 metres
Hence, Option D is correct.
2. Correct Answer: D. ₹30,000
From Question 1, the perimeter of the park is:
200 metres
The fencing cost is ₹150 per metre.
Therefore,
Total fencing cost
= Perimeter × Cost per metre
= 200 × ₹150
= ₹30,000
Hence, the society will spend ₹30,000 on fencing.
Therefore, Option D is correct.
3. Correct Answer: A. 900 sq. metres
First, calculate the total area of the park.
Area of rectangle:
Area = Length × Width
= 60 × 40
= 2,400 sq. metres
The walking track is 5 metres wide on all four sides inside the park.
Therefore, the dimensions of the inner rectangular portion will decrease by 5 metres from both sides.
Inner length:
= 60 − 5 − 5
= 50 metres
Inner width:
= 40 − 5 − 5
= 30 metres
Area of the inner portion:
= 50 × 30
= 1,500 sq. metres
Therefore, area of the walking track:
= Total park area − Inner area
= 2,400 − 1,500
= 900 sq. metres
Hence, Option A is correct.
4. Correct Answer: C. 1,400 sq. metres
After excluding the walking track, the central portion measures:
50 metres × 30 metres
Therefore, its area is:
= 50 × 30
= 1,500 sq. metres
A square flower garden of side 10 metres is constructed within this area.
Area of square:
Area = Side × Side
= 10 × 10
= 100 sq. metres
Therefore, recreational area excluding the flower garden:
= 1,500 − 100
= 1,400 sq. metres
Hence, Option C is correct.
5. Correct Answer: B. ₹1,80,000
From Question 3, the area of the walking track is:
900 sq. metres
The paving tiles cost ₹200 per square metre.
Therefore,
Total paving cost:
= 900 × ₹200
= ₹1,80,000
Hence, the total amount required to pave the walking track is ₹1,80,000.
Therefore, Option B is correct.
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