Estimating the Corridor Repaint
The institute's corridor on the ground floor is to be repainted before an inspection. The corridor is 24 m long, 3.5 m wide and 3 m high. Only the four walls are to be painted; the ceiling and floor are excluded. There are two doors, each 1.2 m by 2.1 m, and four windows, each 1.5 m by 1.2 m; the painter will not paint over them and the full area of each is to be deducted. One coat is specified. The paint covers 8 square metres per litre, and the works committee has instructed that 5 per cent be added for wastage. Vendor A sells only sealed 5-litre packs at ₹220 per litre; Vendor B sells loose paint, any quantity, at ₹240 per litre. Labour is ₹18 per square metre of net painted wall area. GST at 18 per cent is chargeable on paint only, not on labour. The assistant must place the work order with supporting arithmetic, and the officer wants the comparison to be shown, not merely asserted.
1. Compute the net wall area to be painted, showing the deduction working.
Read the worked answer
Step 1 - gross wall area. Perimeter of the corridor = 2 × (24 + 3.5) = 2 × 27.5 = 55 m. Gross wall area = perimeter × height = 55 × 3 = 165 m².
Step 2 - deductions.
- 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 deduction = 5.04 + 7.20 = 12.24 m²
Step 3 - net area. 165 − 12.24 = 152.76 m².
Two checks worth doing before the figure goes on paper: the ceiling (24 × 3.5 = 84 m²) is deliberately not added, and each opening is deducted once only - a common error is to deduct the window area a second time while computing the paint quantity. The net figure of 152.76 m² is the basis for both the paint order and the labour charge, so an error here propagates into every later figure.
2. Work out the paint quantity and decide which vendor to buy from, justifying the choice on the actual bill rather than on the quoted rate.
Read the worked answer
Quantity. 152.76 ÷ 8 = 19.095 litres for one coat. Add 5 per cent wastage: 19.095 × 1.05 = 20.04975 ≈ 20.05 litres.
Vendor A (sealed 5-litre packs at ₹220/litre). Four packs give 20 litres, which is 0.05 litre short of the requirement, so five packs must be bought: 25 litres × ₹220 = ₹5,500. You pay for 4.95 litres that will never be used.
Vendor B (loose, any quantity, at ₹240/litre). 20.05 × ₹240 = ₹4,812.
Decision. Vendor B is cheaper by ₹5,500 − ₹4,812 = ₹688, even though its rate per litre is ₹20 higher.
The judgement point: the visible rate favours A, the actual bill favours B. Pack-size rounding, not the quoted rate, decides this purchase. The margin is ₹688, which is small enough that a second consideration - whether leftover sealed packs can be stored for the next job - could legitimately reverse the choice; if the store can hold them, A's unused 4.95 litres is not really wasted.
3. Using the vendor you selected, compute the total payable including labour and GST, and state the total that would have applied under the other vendor.
Read the worked answer
Vendor B (selected).
- Paint: 20.05 L × ₹240 = ₹4,812.00
- GST on paint at 18%: 4,812 × 0.18 = ₹866.16
- Paint landed cost: 4,812 + 866.16 = ₹5,678.16
- Labour: 152.76 m² × ₹18 = ₹2,749.68 (no GST, per the instruction)
- Total = ₹8,427.84
Vendor A, for comparison.
- Paint: 25 L × ₹220 = ₹5,500.00
- GST: 5,500 × 0.18 = ₹990.00
- Labour: ₹2,749.68
- Total = 5,500 + 990 + 2,749.68 = ₹9,239.68
Saving with Vendor B = 9,239.68 − 8,427.84 = ₹811.84.
Note that the GST widens the gap slightly: the tax is levied on paint value, so A's larger paint bill also attracts ₹123.84 more tax. A common slip is to apply GST to labour as well; the instruction excludes it, and doing so would have inflated both totals by ₹494.94 and made the comparison look different from the one actually approved.