A store sign is a 5 m × 4 m rectangle with a 2 m × 1 m rectangle cut out. Painting cost is ₹180/m². How much will the painting cost for the exposed area?

Correct — A. Paint only what is left after the cut-out.

Whole sign: 5 × 4 = 20 m²
Cut-out: 2 × 1 = 2 m²
Exposed area: 20 − 2 = 18 m²

Cost: 18 × 180 = ₹3,240 → option (a)

Why the others are wrong

• (b)
  ₹3,600 — ₹3,600 is 20 × 180, the cost of the full 5 m × 4 m rectangle. It paints the 2 m² hole that was cut out.
• (c)
  ₹3,960 — ₹3,960 is 22 × 180: the cut-out's 2 m² was added to the sign instead of subtracted.
• (d)
  ₹4,200 — ₹4,200 ÷ 180 ≈ 23.3 m², more than the whole 20 m² sign before anything is removed.

A shape with a piece removed has area = outer area − removed area. Find that area first, then multiply by the rate per m².

Here the rectangle gives 20 m², the hole takes away 2 m², and 18 m² is left to paint at ₹180 each.

Key facts

• Area of a rectangle = length × breadth.
• Area with a cut-out = outer area − area removed.
• Cost = area × rate: 18 m² × ₹180 per m² = ₹3,240.

Common traps

• Adding the cut-out's area instead of subtracting it, which gives ₹3,960.
• Pricing the whole rectangle and forgetting the hole, which gives ₹3,600.

No directly related past PYQ was found.