Pasture rent by cow-months: Four milkmen A, B, C, D used a pasture with different numbers of cows for various months. A’s share of rent is ₹ 720 for grazing 18 cows for 4 months. Using cow × month units, compute the total rent.

Introduction / Context: When usage charges depend on both quantity (number of cows) and time (months), the fair split is proportional to “cow-months.” If we know one person’s charge and their cow-months, we can infer the per-unit rate and then scale up to the total for all users combined.

Given Data / Assumptions:

• A: 18 cows for 4 months ⇒ 72 cow-months; pays ₹ 720.
• B: 25 cows for 2 months ⇒ 50 cow-months.
• C: 28 cows for 5 months ⇒ 140 cow-months.
• D: 21 cows for 3 months ⇒ 63 cow-months.

Concept / Approach: Rate per cow-month = A’s payment / A’s cow-months. Then compute the total cow-months of all four and multiply by the rate to find the total rent.

Step-by-Step Solution:

Verification / Alternative check: Individual implied shares: B ₹ 500, C ₹ 1,400, D ₹ 630, A ₹ 720 ⇒ sum ₹ 3,250, which matches the total computed by the rate method.

Why Other Options Are Wrong: ₹ 3,000, ₹ 1,650, ₹ 3,500, and ₹ 2,750 do not match the consistent per-unit rate derived from A’s known payment and usage.

Common Pitfalls: Averaging cows and months separately; or forgetting to multiply both cows and months to form cow-month units.

Final Answer: ₹ 3250