Choosing tiles for a community hall
A panchayat is flooring a new 12 m × 8 m community hall that will double as an anganwadi room. Two tile sizes have been quoted. The 40 cm × 40 cm tile comes 5 to a box at ₹280 per box; the mason expects about 8% of the area to be lost to edge cutting and breakage. The 60 cm × 60 cm tile comes 4 to a box at ₹540 per box; the mason expects only 5% wastage, because the hall's 12 m length is an exact multiple of 0.6 m and the side rows can be cut from single tiles. Laying charges are ₹70 per m² for the smaller tile (more joints and grout lines) and ₹40 per m² for the larger. The panchayat has sanctioned ₹42,000 for tiles and laying together and cannot exceed it without a fresh resolution. Skirting, adhesive and transport fall under a separate head. The floor is 96 m² and already level, so no levelling cost arises.
1. Compute the total cost of tiles plus laying for both options, showing the area per box, the wastage allowance and the box count.
Read the worked answer
Area to be covered: 12 × 8 = 96 m².
40 cm × 40 cm option
- One tile = 0.40 × 0.40 = 0.16 m²; one box (5 tiles) = 0.80 m².
- Area with wastage = 96 × 1.08 = 103.68 m².
- Boxes = 103.68 ÷ 0.80 = 129.6 → 130 boxes (round up; 129 boxes give only 103.20 m² and fall short).
- Tiles: 130 × 280 = ₹36,400. Laying: 96 × 70 = ₹6,720. Total ₹43,120.
60 cm × 60 cm option
- One tile = 0.36 m²; one box (4 tiles) = 1.44 m².
- Area with wastage = 96 × 1.05 = 100.80 m².
- Boxes = 100.80 ÷ 1.44 = 70 exactly.
- Tiles: 70 × 540 = ₹37,800. Laying: 96 × 40 = ₹3,840. Total ₹41,640.
Note the reversal: the small tile is cheaper per square metre of material (₹350 vs ₹375) yet dearer overall, because 8% wastage and ₹70/m² laying outweigh the rate advantage.
2. Given the ₹42,000 sanction, which option can be adopted? What does this arithmetic hide, and what would you do about it?
Read the worked answer
Only the 60 cm tile fits. ₹41,640 leaves a margin of ₹360; the 40 cm option at ₹43,120 is over the sanction by ₹1,120 and would need a fresh resolution.
What the arithmetic hides.
- The margin is ₹360 - about one and a third boxes. A small rise in the tile rate, a transport charge, or breakage above 5% wipes it out. Get the rate in writing before the resolution is passed.
- 60 cm tiles mean far fewer joints, which matters in an anganwadi where floors are washed and mopped daily; grout lines are where dirt and damp live.
- Against that: larger tiles are heavier, chip more easily in unloading, and offcuts cannot be reused along the walls. A few spare boxes are prudent - but two boxes cost ₹1,080, which the margin cannot absorb, so negotiate a rate reduction or ask for two boxes free.
Best course: adopt the 60 cm option, record the quotation in writing, and keep the ₹360 as a contingency rather than spending it on skirting.
3. A villager says laying the 60 cm tiles diagonally would look better and 'will not change the wastage'. Test that claim at 12% wastage and state the consequence.
Read the worked answer
Test it. Diagonal laying cuts every edge tile at an angle, so offcuts cannot be reused; 12% is a realistic figure, not 5%.
- Area = 96 × 1.12 = 107.52 m².
- Boxes = 107.52 ÷ 1.44 = 74.67 → 75 boxes.
- Tiles: 75 × 540 = ₹40,500. Laying unchanged at ₹3,840. Total ₹44,340.
Consequence: the claim is false. The diagonal layout exceeds the ₹42,000 sanction by ₹2,340 and is also dearer than the plain 40 cm option. It cannot be done without a fresh resolution.
Also note that the original 5% figure rested on the 12 m length being an exact multiple of 0.6 m. Diagonal laying destroys that alignment, so even the plain-laying estimate would have to be re-quoted. The correct answer to the villager is: show the arithmetic, and if the panchayat still wants the pattern, move a resolution for ₹2,340 - do not quietly overspend.