Two Plots, Same Perimeter: The Lease Recommendation
A farmer in a Sehore village offers you a choice between two adjacent plots on a seven-year lease at the same annual rent of ₹96,000. Plot A is rectangular, 40 m by 30 m, but a circular well of radius 3.5 m stands inside it; the well area cannot be cultivated and the lease deed is silent on whether rent is charged on it. Plot B is square, 35 m by 35 m, and is fully cultivable. The lessee must pay for fencing the outer boundary at ₹85 per running metre and for levelling the cultivable area at ₹12 per square metre. The khasra records areas in hectares, and the patwari's copy shows Plot A as 0.12 ha and Plot B as 0.12 ha. The farmer argues: 'Both plots have the same perimeter, so they are of equal value; take either.' He wants your written recommendation within a week and will sign the deed on the basis of it.
1. Calculate the net cultivable area of each plot and determine which plot gives the lower rent per square metre at the same annual rent of ₹96,000. Show every step.
Read the worked answer
Plot A (gross): 40 × 30 = 1,200 m². Well: πr² = 3.1416 × 3.5² = 3.1416 × 12.25 = 38.48 m². Plot A (net cultivable): 1,200 − 38.48 = 1,161.52 m². Plot B: 35 × 35 = 1,225 m².
Rent per m² (₹96,000 ÷ area):
- A: 96,000 ÷ 1,161.52 = ₹82.65 per m²
- B: 96,000 ÷ 1,225 = ₹78.37 per m²
Conclusion: Plot B is cheaper per cultivated square metre by ₹4.28. Expressed the other way, renting B's 1,225 m² at A's rate would cost ₹101,246 - a saving of about ₹5,246 a year, or roughly ₹36,700 over seven years.
Two cautions before signing. First, because the deed is silent on the well, the rent may legally attach to the gross 1,200 m²; in that case A's effective rate is 96,000 ÷ 1,200 = ₹80.00 per m², which narrows but does not close the gap. Second, the well occupies land the lessee pays for but cannot use, so insist the deed expressly excludes the well area or reduces rent accordingly.
2. Evaluate the farmer's claim that equal perimeters mean equal value, using the fencing and levelling costs.
Read the worked answer
Perimeters: A = 2(40 + 30) = 140 m; B = 4 × 35 = 140 m. The claim about perimeter is arithmetically true.
Fencing cost at ₹85/m: A = 140 × 85 = ₹11,900; B = 140 × 85 = ₹11,900. Identical - so fencing cannot decide between them.
But perimeter does not fix area. Of all rectangles with a given perimeter, the square encloses the largest area. Here the gross areas are 1,200 m² and 1,225 m² - B is 25 m² larger on the same 140 m of boundary, and 63.48 m² larger after the well is deducted from A. The farmer has compared the wrong quantity: he compared boundary length, which is equal, when what he is paying for is area, which is not.
Levelling cost at ₹12/m²: A = 1,161.52 × 12 = ₹13,938.24; B = 1,225 × 12 = ₹14,700. B costs ₹761.76 more, one time. Against an annual saving of about ₹5,246, that extra is recovered in under two months of the first year. Over a seven-year lease the difference in levelling cost is negligible.
3. The khasra shows both plots as 0.12 ha. Convert the computed areas into hectares and decide whether a 0.02 ha error in the record could change your recommendation.
Read the worked answer
Conversions (1 ha = 10,000 m²):
- A: 1,161.52 ÷ 10,000 = 0.116152 ha
- B: 1,225 ÷ 10,000 = 0.1225 ha
- Gap: 0.1225 − 0.116152 = 0.006348 ha, i.e. 63.48 m².
The recorded 0.12 ha is a rounded figure for both plots - it overstates A by 0.003848 ha (38.5 m²) and understates B by 0.0025 ha (25 m²). Rounding alone therefore already hides the entire difference between the plots.
A 0.02 ha error equals 200 m². That is more than three times the whole 63.48 m² advantage on which the recommendation rests. So yes - an error of that size could reverse the conclusion, and the difference between the plots is smaller than the precision of the record being relied on.
Action: do not sign on the rounded figure. Have the plots measured, or obtain the field-book (khasra) entry with the survey measurement, before recommending. Do not convert to local bigha for the deed: the bigha varies by region and is not the recorded unit. Record the comparison in hectares, with the measurement source noted.