Painting detail for a barrack block
A work party of 12 sailors is detailed to paint the four exterior walls of a barrack block 60 m long, 20 m wide and 4 m high. Two coats are required on all walls, and doors and windows totalling 40 square metres are not to be painted. The party is assessed to finish the job in 8 days at 8 hours a day. On the morning of the fourth day, after three full days of work, four sailors are transferred to an emergency flood-relief task and do not return. Paint comes in 1-litre containers, each litre covering 25 square metres per coat; the painter's estimate adds 8 per cent for spillage, brush cleaning and uneven surface. A container costs ₹420 and only whole containers can be indented. The junior engineer remarks that had four more sailors been added from the beginning, the job would have been completed in half the scheduled time.
1. Calculate the paintable area, the number of containers to be indented and the paint cost.
Read the worked answer
Wall area = perimeter × height = 2(60 + 20) × 4 = 160 × 4 = 640 m². Deduct openings: 640 − 40 = 600 m² per coat. Two coats: 600 × 2 = 1,200 m² of painting.
Paint at 25 m² per litre = 1,200 ÷ 25 = 48 litres (theoretical). Add 8 per cent wastage: 48 × 1.08 = 51.84 litres. Since only whole containers can be indented, order 52 containers. Rounding down would leave the second coat short.
Cost = 52 × ₹420 = ₹21,840.
2. When will the work actually finish, and how much delay does the transfer cause?
Read the worked answer
Total work = 12 men × 8 days = 96 man-days. Work done in the first three days = 12 × 3 = 36 man-days; balance = 96 − 36 = 60 man-days.
After the transfer, 8 men remain, so remaining time = 60 ÷ 8 = 7.5 days.
Total duration = 3 + 7.5 = 10.5 days, i.e. the job ends at mid-day of the 11th day. Against the 8-day schedule the delay is 2.5 days.
Practical note: this assumes the smaller party works at the same rate and the weather holds; the balance of paint (about 40 per cent of the indent) must be drawn and stored under cover before the second coat begins.
3. Is the junior engineer's statement about adding four sailors at the start correct? Give your reasoning.
Read the worked answer
No. Work is fixed at 96 man-days, so men and days are inversely proportional. With 16 men the duration would be 96 ÷ 16 = 6 days, a saving of 2 days, not half of 8 days.
The claim would only hold if doubling the men halved the work, which is untrue here. In practice 16 men on the same four walls would also get in each other's way, and two coats require drying time between them, so the real duration might be slightly worse than 6 days. The honest reply is: 6 days is the arithmetic limit, and site constraints may push it up, but it will never be the 4 days suggested.