In a dairy farm, 40 cows eat 40 bags of husk in 40 days. Assuming the rate of eating is constant, in how many days will one cow eat one bag of husk?

Introduction / Context:
This question is about resource consumption and uses the concept of cow days similar to man days in work problems. It tests whether you can translate a group consumption rate into an individual rate, and then answer a question about a single cow and a single bag of husk.

Given Data / Assumptions:

• 40 cows consume 40 bags of husk in 40 days.
• The rate of consumption per cow per day is constant.
• We must find how many days 1 cow will take to eat 1 bag of husk.

Concept / Approach:
The key idea is that total consumption can be expressed in cow days of food per bag. We first determine the total consumption in cow days for 40 bags, then compute how many cow days correspond to one bag. Once we know the number of days for one cow to finish one bag, we have our answer.

Step-by-Step Solution:
Step 1: Total cow days of consumption in the given situation is 40 cows * 40 days = 1600 cow days.Step 2: These 1600 cow days correspond to 40 bags of husk.Step 3: Cow days per bag = 1600 / 40 = 40 cow days.Step 4: One cow consuming one bag needs 40 cow days.Step 5: Since one cow supplies one cow day per day, the number of days required = 40 days.

Verification / Alternative check:
Another way is to find the daily quantity of husk eaten. Forty cows eat 40 bags in 40 days, so they eat 1 bag per day as a group. Therefore, in one day each cow eats 1 / 40 of a bag. To finish one whole bag at that rate, a single cow takes 40 days, which matches the earlier calculation.

Why Other Options Are Wrong:
1 day and 10 days are far too small and ignore how slowly a single cow consumes compared to the group. 20 days still halves the correct time. 80 days is double the correct value and would imply that the initial data underestimates the group consumption rate.

Common Pitfalls:

• Confusing bags per day with cow days per bag.
• Assuming that one cow will also take 40 days to eat 40 bags, which confuses per cow and per group quantities.
• Skipping the step of finding the total cow days and directly guessing an answer.

Final Answer:
One cow will take 40 days to eat one bag of husk.