In a dairy farm, $40$ cows eat $40$ bags of husk in $40$ days. In how many days one cow will eat one bag of husk?

### Concept & Chain Rule This is a classic variation of the "men, days, work" formula, replacing men with cows and work with bags eaten. $$ \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} $$ ### Step-by-Step Solution * **Given**: - $M_1 = 40$ cows, $W_1 = 40$ bags, $D_1 = 40$ days - $M_2 = 1$ cow, $W_2 = 1$ bag, $D_2 = x$ days * **Calculation**: $$ \frac{40 \times 40}{40} = \frac{1 \times x}{1} $$ $$ 40 = x $$ ### Exam Strategy & Shortcut If $40$ cows take $40$ days to eat $40$ bags, each cow is assigned exactly $1$ bag to eat over the course of those $40$ days. Therefore, $1$ cow takes the full $40$ days to eat $1$ bag. ### Common Pitfall The intuitive trap: assuming that if the number of cows and bags is reduced to $1$, the number of days must also proportionally reduce to $1$. Time does not scale linearly with equal workforce and workload reductions. ### Final Answer Therefore, the correct answer is **40**.