2014 AMC 10A Problem 6

We have to multiply $b$ by $\dfrac{d}{a}$ to account for the new number of cows. We then have to multiply by $\dfrac{e}{c}$ to account for the new time that we have. This gives us a final answer of $$b \cdot \dfrac{d}{a} \cdot \dfrac{e}{c} = \dfrac{bde}{ac}.$$ Thus, A is the correct answer.