Field Measurement, Budget Allocation and Seed Estimate
An extension worker must prepare a work and input estimate for three adjoining patches before the monsoon. Patch A is rectangular, 200 m × 120 m. Patch B is a square of side 150 m. Patch C is triangular, with a base of 240 m and a perpendicular height of 150 m. Hand-level readings give slopes of 2% for A, 6% for B and 9% for C. The department can release ₹1,00,000 this year for trench-cum-bund work, and the current schedule of rates works out to ₹20,000 per hectare treated. In this hamlet a 3 m wide strip along the inside of every boundary of a rectangular plot is left unploughed for a grassed bund; triangular plots carry no such strip. Green gram is to be sown on the treated area at 20 kg/ha, with 10% extra seed kept back for gap filling and border rows, and seed costs ₹110 per kg. The seed bill has to come out of the same ₹1,00,000.
1. Compute the area of each patch and the net sown area of Patch A after the boundary strips are deducted.
Read the worked answer
Patch A: 200 × 120 = 24,000 m² = 2.40 ha. Net of the 3 m strip on all four inner sides: (200 − 6) × (120 − 6) = 194 × 114 = 22,116 m² = 2.2116 ha, so the strip takes 0.1884 ha, about 7.9% of the plot.
Patch B: 150 × 150 = 22,500 m² = 2.25 ha. No strip is deducted, since the rule is given for rectangular plots only.
Patch C: ½ × 240 × 150 = 18,000 m² = 1.80 ha.
Total = 2.40 + 2.25 + 1.80 = 6.45 ha. Net cultivable area after the A strip = 6.45 − 0.1884 = 6.2616 ha.
Note the arithmetic trap: the strip reduces both length and width, so it must be subtracted twice from each dimension; subtracting one 3 m band from the perimeter, or deducting 3 m only once, overstates the area. Also state clearly whether the treatment rate applies to gross or net area - for trench-cum-bund the bunds occupy the strip, so gross area is the right base for costing.
2. Allocate the ₹1,00,000 across the three patches and justify the priority order.
Read the worked answer
Capacity: ₹1,00,000 ÷ ₹20,000/ha = 5.00 ha of treatment against 6.45 ha available.
Priority by erosion risk, not by area or convenience. Slope steepness drives soil loss far more than area does, so C (9%) comes first, then B (6%), then A (2%).
C: 1.80 ha × ₹20,000 = ₹36,000. B: 2.25 ha × ₹20,000 = ₹45,000. Running total ₹81,000 for 4.05 ha, leaving ₹19,000, which buys 0.95 ha of A.
The result is 5.00 ha treated and 1.45 ha of A left. Two judgement points should be stated rather than hidden. First, treating 0.95 ha of a 2.4 ha field leaves a fragment; either treat A's lower, outfall end as a unit or defer A entirely and carry ₹19,000 forward, because a partial bund on a gentle slope gives little return. Second, if A adjoins the hamlet's drinking-water tank or the main footpath, that changes the order and the reason should be written down. Record the assumption, not just the number.
3. Recompute the plan when the seed cost must be met from the same ₹1,00,000. What changes and what would you tell the farmers?
Read the worked answer
Seed is needed only on the area actually treated, so the two costs are linked and must be solved together, not sequentially.
Let T be the treated area in hectares. Works cost = 20,000 T. Seed = 20 kg/ha × 1.10 × ₹110 = ₹2,420 per hectare. Total per hectare = ₹22,420. So T = 1,00,000 ÷ 22,420 = 4.46 ha.
Check: C 1.80 ha + B 2.25 ha = 4.05 ha, costing 4.05 × 20,000 = ₹81,000 in works and 4.05 × 2,420 = ₹9,801 in seed, total ₹90,801. Balance ₹9,199 buys 9,199 ÷ 22,420 = 0.41 ha of A.
So treatment falls from 5.00 ha to about 4.46 ha, and the shortfall lands on the least erodible patch, exactly where it should.
Tell the farmers plainly: the budget covers C and B in full and about 0.4 ha of A; seed will be issued against the measured treated area, not against the area applied for, and the 10% gap-filling seed stays with the village-level worker for re-sowing after establishment.