The Ward That Had Three Tankers
Ward 12 of a municipal corporation serves 4,200 households. The public health norm is 40 litres per household per day, and the ward has committed to meeting it entirely by tanker while the piped main is repaired. Three hired tankers, each of 9,000 litres, run out of a filling station 13 km away. A round trip takes 1.5 hours of driving and 0.5 hour of filling and queuing, so each tanker's 8-hour shift covers exactly four trips. Diesel costs ₹92 a litre and each tanker runs 4 km to the litre. A driver is paid ₹600 per 8-hour shift; any hour beyond that is paid at 1.5 times the hourly rate. Tanker hire is ₹4,500 per tanker per day. The ward's tanker budget is ₹9.6 lakh for a 30-day month, and the current deployment delivers only four trips per tanker per day. The ward councillor has asked for a written note before the standing committee meets on Friday.
1. Calculate the daily demand, the current supply, and the shortfall in kilolitres and as a percentage. Then state the minimum number of trips per day that would meet demand, and what that implies per tanker.
Read the worked answer
Demand: 4,200 households × 40 L = 168,000 L = 168 kL per day.
Current supply: 3 tankers × 9 kL × 4 trips = 108 kL per day.
Shortfall: 168 − 108 = 60 kL per day, which is 60 ÷ 168 = 35.7% of demand. The ward is meeting roughly two-thirds of its own norm.
Trips needed: 168 ÷ 9 = 18.67, so trips must be a whole number: 19 trips, delivering 171 kL and leaving 3 kL of slack. Nineteen trips cannot be shared evenly across three tankers (19 ÷ 3 = 6.33), so the working split is 7 + 6 + 6. Each tanker must therefore add 2 to 3 trips on top of the 4 that fit inside an 8-hour shift - that is where the cost question comes from, because every extra trip is 2 hours, and the 7-trip tanker will run 14 hours. A note that says only 'increase trips' without naming the 7/6/6 split hides the fact that one driver alone absorbs 6 hours of overtime.
2. Cost the 19-trip plan for a 30-day month - diesel, tanker hire, driver wages and overtime - and say whether ₹9.6 lakh covers it.
Read the worked answer
Overtime. Split 7/6/6 gives shift lengths of 14, 12 and 12 hours, so overtime is 6 + 4 + 4 = 14 hours a day. Hourly wage = ₹600 ÷ 8 = ₹75; overtime rate = 1.5 × 75 = ₹112.50. Daily overtime cost = 14 × 112.50 = ₹1,575; monthly = ₹47,250.
Diesel. 19 trips × 26 km = 494 km a day. At 4 km/L that is 123.5 L, and at ₹92/L = ₹11,362 a day, or ₹340,860 a month.
Hire. 3 × ₹4,500 × 30 = ₹405,000.
Base wages. 3 × ₹600 × 30 = ₹54,000.
Total: 340,860 + 405,000 + 54,000 + 47,250 = ₹847,110, inside the ₹9.6 lakh budget with ₹112,890 to spare - about 12% headroom.
Two cautions belong in the note: the surplus is under one month's hire of a fourth tanker, and it disappears if tankers lose days to breakdowns or if diesel crosses roughly ₹118/L. The plan is affordable but not comfortable.
3. A councillor proposes hiring a fourth tanker and running five trips each (20 trips a day) so that no driver works more than 10 hours. Test that proposal against the budget and recommend between it and the 19-trip plan.
Read the worked answer
| Head | 19-trip plan | Fourth tanker (20 trips) |
|---|---|---|
| Diesel | ₹340,860 | 20 × 26 = 520 km → 130 L → ₹11,960/day = ₹358,800 |
| Hire | ₹405,000 | 4 × 4,500 × 30 = ₹540,000 |
| Base wages | ₹54,000 | 4 × 600 × 30 = ₹72,000 |
| Overtime | ₹47,250 | 5 trips = 10 h, so 2 h × 4 drivers = 8 h/day → ₹900/day = ₹27,000 |
| Total | ₹847,110 | ₹997,800 |
The fourth tanker exceeds the ₹9.6 lakh budget by ₹37,800 and buys only 9 kL of extra water that the ward does not need (demand is 168 kL). Its one real merit is safety: a 10-hour shift instead of 14. That merit can be bought far more cheaply - keep the 19-trip plan, but rotate which tanker takes the 7-trip day so no driver does 14 hours twice running, and hold the ₹1.12 lakh surplus as an overtime and breakdown reserve. If the standing committee wants the fourth tanker anyway, the note should say plainly that it requires a supplementary of about ₹38,000 a month, or a cut of roughly 6 L per household (168 kL down to 159.6 kL, i.e. 18 trips) to pay for it.