A rectangular park is $120 ext{ m}$ long and $104 ext{ m}$ wide. A $1 ext{-m}$ wide path runs along the boundary of the park, remaining completely inside the park area. Thus, the outside edges of the path run along the boundary wall of the park. The inside edges of the path are marked with a white line of negligible thickness. If it costs ₹2.50 to mark each metre with the white line, then how much would it cost (in ₹) to fully mark the inside edges of the path?

Question

A rectangular park is $120 	ext{ m}$ long and $104 	ext{ m}$ wide. A $1	ext{-m}$ wide path runs along the boundary of the park, remaining completely inside the park area. Thus, the outside edges of the path run along the boundary wall of the park. The inside edges of the path are marked with a white line of negligible thickness. If it costs ₹2.50 to mark each metre with the white line, then how much would it cost (in ₹) to fully mark the inside edges of the path?

Accepted Answer

**Solution:**

1. Given dimensions of the park:
   - Length = $120 	ext{ m}$
   - Width = $104 	ext{ m}$

2. The path is $1 	ext{ m}$ wide and runs inside the park along the boundary.

3. Therefore, the dimensions of the inner rectangle (inside edge of the path) are:
   - Length = $120 - 2 	imes 1 = 118 	ext{ m}$
   - Width = $104 - 2 	imes 1 = 102 	ext{ m}$

4. Calculate the perimeter of the inner rectangle (inside edge of the path):
   $$	ext{Perimeter} = 2 	imes (118 + 102) = 2 	imes 220 = 440 	ext{ m}$$

5. Cost to mark each metre = ₹2.50

6. Total cost to mark the inside edge:
   $$440 	imes 2.50 = ₹1100$$

**Answer:** ₹1100

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