Comparing Two Painting Quotes for a Community Hall
The gram panchayat of a village near Bhagalpur has sanctioned a community hall with internal dimensions 12 m × 9 m × 4 m (height). The walls and the ceiling are to be painted, and the floor is to be tiled with square tiles of side 0.6 m. There are two doors of 1.2 m × 2.1 m each and four windows of 1.5 m × 1.2 m each. Painter A quotes ₹18 per square metre and says he will charge for the entire wall surface and the ceiling, ignoring the door and window openings, because the cutting and edging takes the same time. Painter B quotes ₹22 per square metre but deducts all openings. The mukhiya must place the work order this week. Tiles cost ₹85 each, and the mason advises buying 5% extra for cutting and breakage. The panchayat's own rough estimate had assumed a painting cost of about ₹5000.
1. Calculate the true paintable area: the net wall surface after all openings, plus the ceiling.
Read the worked answer
Wall area = perimeter × height = 2(12 + 9) × 4 = 42 × 4 = 168 m². Ceiling = 12 × 9 = 108 m².
Openings:
- Doors: 2 × (1.2 × 2.1) = 2 × 2.52 = 5.04 m²
- Windows: 4 × (1.5 × 1.2) = 4 × 1.80 = 7.20 m²
- Total openings = 12.24 m²
Net wall area = 168 − 12.24 = 155.76 m². Net paintable area = 155.76 + 108 = 263.76 m².
Painter A's basis is the gross 168 + 108 = 276 m². The difference, 12.24 m², is only 4.4% of the gross area - a fact worth keeping in mind before comparing rates.
2. Compare the two quotations and recommend one. Would your recommendation change if Painter A agreed to deduct the openings?
Read the worked answer
Painter A: 276 × ₹18 = ₹4968. Painter B: 263.76 × ₹22 = ₹5802.72.
A is cheaper by ₹834.72, even though he bills for 12.24 m² he will never touch. The reason is that his rate is lower by ₹4 per m² (22.2%), while the disputed area is only 4.4% of the whole. A rate difference outweighs an area concession here, so the superficial reasoning 'B is fairer because he deducts the windows' gives the wrong financial answer. Recommend A.
If A agrees to deduct the openings: 263.76 × ₹18 = ₹4747.68, a further saving of ₹220.32, making it the cheapest of the three possibilities. So the mukhiya should place the order with A and use the deduction as a bargaining point, not as the deciding factor.
3. How many tiles must be purchased and what will they cost? Is the 5% allowance really needed here?
Read the worked answer
Floor area = 12 × 9 = 108 m². Each tile = 0.6 × 0.6 = 0.36 m². Tiles needed = 108/0.36 = 300 (an exact whole number). With 5% wastage: 300 × 1.05 = 315 tiles. Cost = 315 × ₹85 = ₹26,775.
On the judgement question: since 12/0.6 = 20 and 9/0.6 = 15 exactly, the hall can be laid out in whole tiles in both directions, so almost no cutting waste arises at the edges. The 5% is therefore insurance against breakage and site damage rather than a genuine cutting requirement - 300 tiles plus a couple of spare boxes would be enough, and buying the full 15 extra is a small but avoidable excess.