Algebraic cost comparison with two purchase mixes A man buys 3 cows and 18 goats for ₹47,200. Instead, if he had purchased 8 cows and 3 goats, the second mix would cost ₹53,000 more than the first. Based on these two linear conditions, determine the cost of one cow (assume prices are constant per animal and rounded to the nearest thousand rupees as per the given options).

Introduction / Context:
This problem encodes two purchase combinations of cows and goats into simultaneous linear equations. By forming equations for the total costs of the two mixes and comparing them, we isolate the unit price of a cow. Because the stated “₹53,000 more” makes the exact goat price non-integer, we use Recovery-First reasoning and round to the nearest thousand rupees to match realistic option steps and typical exam intent.

Given Data / Assumptions:

• Let cow price = C and goat price = G (in rupees).
• 3C + 18G = 47200.
• 8C + 3G costs ₹53,000 more than ₹47,200, so 8C + 3G = 100200.
• Objective: estimate C to the nearest thousand rupees (options are spaced by ₹1,000).

Concept / Approach:
Set up and solve the pair of linear equations. If the algebra yields a non-round goat price (common with market-mix wordings), pick the cow price consistent with the computed value and nearest to the given option grid. This preserves the core quantitative idea without changing numbers.

Step-by-Step Solution:
Equation 1: 3C + 18G = 47200.Equation 2: 8C + 3G = 100200.Eliminate C by scaling: 24C + 144G = 377600 (Eq.1 × 8) and 24C + 9G = 300600 (Eq.2 × 3).Subtract: (24C + 144G) − (24C + 9G) = 377600 − 300600 ⇒ 135G = 77000 ⇒ G ≈ 570.37.Back-substitute to get C: from 8C + 3G = 100200 ⇒ 8C = 100200 − 3(570.37) ≈ 98488.9 ⇒ C ≈ 12311.1.Nearest option-thousand to ₹12,311 is ₹12,000.

Verification / Alternative check:
Using C = ₹12,000 gives 3C + 18G = 47200 ⇒ 18G = 11200 ⇒ G ≈ ₹622. This produces a second-mix difference close to the stated “₹53,000 more” (actual ≈ ₹50,667). The discrepancy is small relative to option spacing and consistent with rounding/statement tolerance often seen in such items.

Why Other Options Are Wrong:
₹10,000 and ₹11,000 force goat prices that make the second-mix price gap far from ₹53,000. ₹13,000 overshoots and implies a difference well above ₹53,000. ₹9,000 is even further off.

Common Pitfalls:
Interpreting “more” as total cost instead of the difference; forgetting to eliminate variables properly; expecting exact integers when the stem implicitly allows rounding to option granularity.

Final Answer:
₹ 12,000