How Many Drums of Distemper for the Workshop Hall?
A polytechnic must paint its workshop hall before an inspection. The hall is 20 m long, 12 m wide and 4.5 m high. It has four windows of 1.5 m × 1.2 m and two doors of 2.5 m × 1.2 m. The walls are to receive two coats of distemper supplied in 20 litre drums at ₹3,200 per drum; the ceiling also gets two coats, but of a different emulsion supplied in 10 litre packs at ₹1,450 per pack. The distemper covers 4 m² per litre per coat, the emulsion covers 6 m² per litre per coat, and the painter adds 8 per cent to the wall quantity and 10 per cent to the ceiling quantity for wastage and surface unevenness. The accounts section has already issued a purchase indent for five drums of distemper and nine packs of emulsion, and the painter says 'we will manage, there is always something left in the last drum'. The junior engineer must sign the indent today.
1. Calculate the net wall area and the distemper actually required for two coats with wastage.
Read the worked answer
Perimeter = 2(20 + 12) = 64 m; gross wall area = 64 × 4.5 = 288 m².
Deductions: windows 4 × (1.5 × 1.2) = 7.2 m²; doors 2 × (2.5 × 1.2) = 6.0 m²; total 13.2 m².
Net wall area = 288 − 13.2 = 274.8 m².
Two coats = 549.6 m² of painted surface; with 8 per cent wastage = 549.6 × 1.08 = 593.6 m².
At 4 m² per litre per coat, litres = 593.6 / 4 = 148.4 L.
Drums = 148.4 / 20 = 7.42, so 8 drums (160 L) must be bought, costing ₹25,600. The indent of five drums (100 L) is short by about 48 L - nearly two and a half drums, not 'a little left in the last one'. Signing it would stop the work halfway up a wall.
2. Show what error would have produced the indent of five drums, and why it is a plausible mistake.
Read the worked answer
Five drums = 100 L, which at 4 m² per litre covers 400 m² of surface; allowing 8 per cent wastage, the assumed painted area was about 400 / 1.08 = 370 m².
The clean explanation is that the second coat was dropped. One coat on 274.8 m² needs 274.8 / 4 = 68.7 L; adding 8 per cent gives 74.2 L, which rounds to 4 drums, and a rough mental allowance for edges and pillars takes it to 5. The indent is therefore the single-coat figure with margin.
This is the commonest error in painting estimates: the coverage rate is quoted per coat, and the number of coats is forgotten. The rate sheet says 'per litre per coat' for exactly this reason, and the checking engineer should always multiply by the number of coats before rounding up to whole containers.
3. Check the ceiling requirement and state exactly what you would sign.
Read the worked answer
Ceiling area = 20 × 12 = 240 m², with no deductions.
Two coats = 480 m²; with 10 per cent wastage = 528 m².
At 6 m² per litre per coat, litres = 528 / 6 = 88 L; in 10 L packs that is 8.8, so 9 packs (90 L) at ₹1,450 = ₹13,050. The indent of nine packs is correct, which shows the ceiling was worked out properly while the wall second coat was overlooked.
What to sign: amend the distemper line to 8 drums (₹25,600) and retain 9 emulsion packs (₹13,050) - total ₹38,650. Do not buy 5 now and top up later: a different batch can show a shade difference on the same wall. Eight drums leave about 11.6 L for touch-up. Add the note 'rate is per coat; two coats computed' beside the signature so the arithmetic is auditable.