A cow costs more than 4 goats but less than 5 goats. If a goat costs between ` 600 and ` 800, which of the following is a most valid conclusion?

The correct option is: A cow costs between ₹2,400 and ₹4,000.

Step-by-step Explanation:

Let us define variables to represent the costs of the animals:
Let $C$ represent the cost of a cow.
Let $G$ represent the cost of a goat.

From the problem description, we are given two key relationships:

1. The cost of a cow is more than the cost of 4 goats but less than the cost of 5 goats. This can be expressed as the following compound inequality:
$4G<C<5G$

2. The cost of a goat is between ₹600 and ₹800:
$600<G<800$

To determine the range of the cow's cost ($C$), we calculate its minimum and maximum possible bounds:

1. Calculating the Lower Bound:
We know that $C>4G$. Since the cost of a goat ($G$) is strictly greater than ₹600, the lower limit for the cow's cost is:
$C>4\times 600=2400$
Thus, the cow must cost more than ₹2,400.

2. Calculating the Upper Bound:
We know that $C<5G$. Since the cost of a goat ($G$) is strictly less than ₹800, the upper limit for the cow's cost is:
$C<5\times 800=4000$
Thus, the cow must cost less than ₹4,000.

Conclusion:
Combining the lower and upper bounds, we establish the range for the cost of a cow:
$2400<C<4000$
Therefore, the most valid conclusion is that a cow costs between ₹2,400 and ₹4,000.