Correct Option (D)
The problem establishes two conditions: first, a cow's cost is greater than that of 4 goats but less than that of 5 goats; second, a goat's cost lies between ₹ 600 and ₹ 800.
- To determine the minimum possible cost of a cow, we calculate the minimum cost for 4 goats: 4 goats × ₹ 600/goat = ₹ 2,400.
- To determine the maximum possible cost of a cow, we calculate the maximum cost for 5 goats: 5 goats × ₹ 800/goat = ₹ 4,000.
Therefore, the cost of a cow (C) must satisfy the inequality ₹ 2,400 < C < ₹ 4,000. Option (D) states that a cow costs between ₹ 2,400 and ₹ 4,000, which accurately represents the full range of possible costs for the cow based on the given information, making it the most valid conclusion.
Incorrect Options:
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Option (A): A cow costs more than ₹ 2,500. While this statement is factually true given that the minimum cost is ₹ 2,400, it is not the most comprehensive conclusion. It fails to provide an upper bound for the cow's cost and does not establish the tightest possible lower bound.
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Option (B): A cow costs less than ₹ 3,600. This statement is incorrect. The maximum possible cost for a cow is less than ₹ 4,000. This range includes values such as ₹ 3,700 or ₹ 3,900, which are not less than ₹ 3,600.
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Option (C): A cow costs between ₹ 2,600 and ₹ 3,800. This range is narrower than the actual possible range of ₹ 2,400 to ₹ 4,000. It incorrectly excludes potential cow costs between ₹ 2,400 and ₹ 2,600 (e.g., ₹ 2,500) and between ₹ 3,800 and ₹ 4,000 (e.g., ₹ 3,900). Consequently, it is not the most accurate or complete conclusion.