Tank, Solar Pump and the Cost of a Shortfall
Ward 7 of a village panchayat has a 15,000-litre overhead tank, which holds 4,000 litres at 6 a.m. The solar pump runs from 9 a.m. to 4 p.m. and delivers 1,200 litres an hour. Water is distributed through one outlet that draws 1,500 litres an hour during the morning slot (6–8 a.m.) and the evening slot (5–7 p.m.). The ward has 240 households, and the panchayat norm is 45 litres per household per day. The tank level must never fall below 500 litres, because below that the outlet loses pressure. A diesel borewell that delivers 800 litres an hour can be run only between 10 a.m. and 5 p.m., and costs 150 rupees an hour to run. A private tanker charges 350 rupees per 1,000 litres. The secretary must place either a borewell or a tanker order for the next 30 days.
1. Compute the water actually delivered in a day, the daily shortfall, and the borewell hours and cost for 30 days. Compare this with the tanker option.
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Daily balance. 6 a.m.: 4,000 L. Morning draw 1,500 × 2 = 3,000 L, leaving 1,000 L at 8 a.m. (above the 500 L floor). Solar input 1,200 × 7 = 8,400 L, so 9,400 L at 4 p.m. Evening draw 3,000 L, leaving 6,400 L at 7 p.m.
Delivered = 3,000 + 3,000 = 6,000 L. Demand = 240 × 45 = 10,800 L. Shortfall = 4,800 L.
Borewell. 4,800 ÷ 800 = 6 hours, which fits the 10 a.m.–5 p.m. window. Cost = 6 × 150 = 900 rupees a day, or 27,000 rupees for 30 days. It can run 10 a.m.–4 p.m. without overflow: the level is 2,200 L at 10 a.m. and the combined inflow of 2,000 L an hour for 6 hours takes it to 14,200 L, under the 15,000 L capacity.
Tanker. 4.8 × 350 = 1,680 rupees a day, or 50,400 rupees for 30 days. The borewell saves 23,400 rupees over the month.
2. The panchayat decides to cut the norm to 40 litres per household per day. Recompute the shortfall, the borewell hours and the 30-day borewell cost.
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New demand. 240 × 40 = 9,600 L a day. Supply is unchanged at 6,000 L, so the shortfall becomes 9,600 − 6,000 = 3,600 L.
Borewell hours. 3,600 ÷ 800 = 4.5 hours, still inside the permitted 10 a.m.–5 p.m. window. A convenient schedule is 10 a.m. to 2.30 p.m., which also avoids any risk of the tank approaching its 15,000 L ceiling.
Cost. 4.5 × 150 = 675 rupees a day; for 30 days, 675 × 30 = 20,250 rupees, against 27,000 rupees at the 45-litre norm. The 5-litre reduction therefore saves 6,750 rupees a month in running cost and 1,200 litres of demand a day.
Check on the floor level. With the borewell running in the morning, the tank level never drops below 1,000 L at 8 a.m., so the 500 L pressure floor is respected throughout.
3. A tanker owner offers 300 rupees per 1,000 litres for a firm 30-day order at 4,800 litres a day. At what tanker rate would the tanker become cheaper than the borewell? Advise the secretary.
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Compare at 4,800 L a day. The borewell costs 900 rupees a day for 4,800 litres, which is 900 ÷ 4.8 = 187.50 rupees per 1,000 litres. At the offered rate of 300 rupees per 1,000 litres the tanker costs 4.8 × 300 = 1,440 rupees a day, or 43,200 rupees for 30 days - still 16,200 rupees more than the borewell.
Break-even. The tanker only matches the borewell below 187.50 rupees per 1,000 litres; below that figure it wins, above it the borewell wins. A rate of 300 rupees is about 60 per cent higher than break-even.
Advice. Place the borewell order. The tanker should be kept only as a standby for days when the borewell is under repair, and even then it should be hired by the trip, not on a 30-day commitment. If the panchayat can cut demand to 40 litres per household, the borewell cost falls further to 20,250 rupees and the case for it becomes stronger still.