Boro paddy water balance and a second-hand tractor offer
A farmer in Purba Bardhaman has 2.0 ha of boro paddy on a sandy loam that percolates freely. Water is lifted from a canal-side pit by a 3 HP diesel pump set that delivers about 8 L/s at his working head of 20 m. He runs the pump 6 hours a day and conveys water 45 m through an unlined earthen channel; his measurement shows about 30% of the pumped volume is lost in the channel. In the last week of April the crop's peak water requirement, including percolation, is 8 mm/day. Diesel costs ₹92 per litre and the pump uses 0.6 litre per hour. He is also being offered a second-hand 35 HP tractor with a rotavator for ₹3.2 lakh; the custom-hiring centre at the block charges ₹2,200 per hectare for puddling, but queues are long in the peak week. He wants to know whether to rebuild the channel, buy a bigger pump, or buy the tractor.
1. Does the present pump meet peak demand? Show the daily water balance in cubic metres and millimetres, then rank the three options.
Read the worked answer
Water balance (peak week)
- Pumped per day: 8 L/s × 6 h × 3600 = 172,800 L = 172.8 m³.
- After 30% channel loss: 172.8 × 0.70 = 121 m³ reaching the field.
- Crop demand: 8 mm/day × 10,000 m²/ha × 2 ha = 160 m³/day (80 m³/ha).
- Supply per hectare: 121 ÷ 2 = 60.5 m³/ha = 6.05 mm/day against 8 mm/day - a shortfall of about 1.95 mm/day, roughly 24%.
Options ranked
- Extend running hours now (cheapest). Required gross volume = 160 ÷ 0.70 = 228.6 m³; at 28.8 m³/h that is 7.9 h/day. Running 8 h costs an extra 2 h × 0.6 L × ₹92 ≈ ₹110/day and needs no capital.
- Line the channel (best seasonal return). At 10% loss, 6.2 h/day delivers the same water; diesel falls from 6 × 0.6 × 92 = ₹331 to about ₹340 for 6.2 h… in practice he runs 8 h and banks a margin. Over a 60-day peak, cutting losses saves roughly ₹6,000–9,000 per season against a lining cost of ₹20,000–25,000, so it pays back in about three seasons and also reduces labour.
- Bigger pump - not justified. Capital cost and higher diesel per hour solve a problem the channel is creating.
So: extend hours immediately, line the channel before the next boro season, and keep the 3 HP set.
2. Evaluate the tractor purchase: show fixed and variable costs against the custom rate, and state the condition under which buying would become rational.
Read the worked answer
Fixed cost per year
- Depreciation: (₹3,20,000 − ₹64,000 salvage at 20%) ÷ 10 = ₹25,600
- Interest at 10% on about half the capital: ≈ ₹16,000
- Insurance and shed: ₹9,000
- Total fixed ≈ ₹50,600 per year
Variable cost and work rate
- Diesel 4 L/h × ₹92 = ₹368; operator ₹150; lubricant and repairs ₹80 → ≈ ₹600/h
- Rotavator output ≈ 0.35 ha/h → ₹1,714 per pass, ₹3,430/ha for two passes
Comparison: custom puddling is ₹2,200/ha. Even ignoring the ₹50,600 fixed cost, his own variable cost of ₹3,430/ha exceeds the custom rate, so for 2 ha the tractor can never be cheaper. Total ownership cost at 2 ha would be about ₹28,700/ha.
When it becomes rational: only as a custom-hiring business. Contribution per hired hour is ₹1,000 − ₹600 = ₹400, so fixed cost is covered at ₹50,600 ÷ ₹400 ≈ 127 paid hours per year. Advise him to buy only if he can secure roughly 130+ hours of assured outside work, and to have the second-hand machine inspected for engine hours, hydraulic lift and rotavator gearbox before paying - a breakdown in the peak week is the real risk, not the price.
3. The custom-hiring queue is unreliable in the peak week. What practical measures reduce timeliness risk without buying the tractor?
Read the worked answer
Treat timeliness as a scheduling problem, not a machinery-purchase problem.
- Book the custom centre in the first week of the booking window and get a written slot date; queue position, not price, is the risk.
- Stagger transplanting across 2 ha in three blocks about 7–10 days apart, so puddling and transplanting peaks do not coincide for the whole area.
- Keep a 0.2–0.3 ha nursery block close to the water source so that late puddling does not strand seedlings.
- Arrange a standby: negotiate with a neighbouring farmer who owns a tractor for a fixed per-hectare rate with a fallback date, or hire a power tiller with cage wheels for the earliest block.
- Keep the channel and field channels clean before the peak so that a machine arriving late still finishes in one pass; a waterlogged approach channel wastes hired hours.
Decision rule: if late puddling typically costs more than about ₹3,400/ha in lost yield - the gap between custom and own-machine variable cost - and happens in most years, revisit ownership as a joint purchase with two or three farmers rather than a sole purchase.