Question:
Inside a rectangular park of dimensions 100m × 80m, walking paths 3m wide are to be constructed as shown in the figure given below (a 3m-wide border path runs around all four sides of the park, plus one 3m-wide path down the vertical centre and one 3m-wide path across the horizontal centre, dividing the interior lawn into four equal rectangular plots). Find the cost of construction of paths at the rate of ₹ 120/m².
Inside a rectangular park of dimensions 100m × 80m, walking paths 3m wide are to be constructed as shown in the figure given below (a 3m-wide border path runs around all four sides of the park, plus one 3m-wide path down the vertical centre and one 3m-wide path across the horizontal centre, dividing the interior lawn into four equal rectangular plots). Find the cost of construction of paths at the rate of ₹ 120/m².
Updated On: Sep 16, 2026
- ₹ 1,82,580
- ₹ 1,84,260
- ₹ 1,84,680
- ₹ 1,85,400
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The Correct Option is C
Solution and Explanation
Concept:
Step 1: Find the interior region left after removing the 3 m border on all sides
Park = 100 m x 80 m, border width = 3 m on each side
Interior length = 100 - 2(3) = 94 m
Interior breadth = 80 - 2(3) = 74 m
Interior area = 94 x 74 = 6956 m²
Step 2: Find the area of the two crossing paths inside this interior region
Vertical path (3 m wide, full interior breadth) = 3 x 74 = 222 m²
Horizontal path (3 m wide, full interior length) = 3 x 94 = 282 m²
These overlap in a 3 x 3 square, counted twice, so subtract it once: overlap = 9 m²
Total crossing path area = 222 + 282 - 9 = 495 m²
Step 3: Find the lawn area and then the total path area
Lawn area = Interior area - crossing path area = 6956 - 495 = 6461 m²
Total park area = 100 x 80 = 8000 m²
Total path area (border + crossing) = 8000 - 6461 = 1539 m²
Step 4: Find the cost of construction
Cost = 1539 x 120 = ₹1,84,680
Final Answer: ₹1,84,680
- Break the park into the outer border path and the two crossing paths inside, taking care not to double-count the small square where the crossing paths overlap.
- Total path area = Total park area - Area of the leftover lawn plots.
- Once the total path area is known, multiply by the rate per m² to get the cost.
Step 1: Find the interior region left after removing the 3 m border on all sides
Park = 100 m x 80 m, border width = 3 m on each side
Interior length = 100 - 2(3) = 94 m
Interior breadth = 80 - 2(3) = 74 m
Interior area = 94 x 74 = 6956 m²
Step 2: Find the area of the two crossing paths inside this interior region
Vertical path (3 m wide, full interior breadth) = 3 x 74 = 222 m²
Horizontal path (3 m wide, full interior length) = 3 x 94 = 282 m²
These overlap in a 3 x 3 square, counted twice, so subtract it once: overlap = 9 m²
Total crossing path area = 222 + 282 - 9 = 495 m²
Step 3: Find the lawn area and then the total path area
Lawn area = Interior area - crossing path area = 6956 - 495 = 6461 m²
Total park area = 100 x 80 = 8000 m²
Total path area (border + crossing) = 8000 - 6461 = 1539 m²
Step 4: Find the cost of construction
Cost = 1539 x 120 = ₹1,84,680
Final Answer: ₹1,84,680
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