If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?

Let $$M$$ be the total number of mice killed, $$c$$ be the number of cats, $$i$$ be the number of days and $$e$$ be the average number of mice killed by one cat in one day.

The number of mice killed is proportional to both the number of cats and the number of days.

=> $$m=ice$$

Substituting $$M=100$$, $$i=100$$ and $$c=100$$ into this equation, we find :

=> $$100=100 \times 100 \times e$$

=> $$e=\frac{1}{100}$$

Thus,  substituting $$M=4$$ , $$c=4$$ and $$e=\frac{1}{100}$$ to get:

=> $$4=i \times 4 \times \frac{1}{100}$$

=> $$i=100$$ days

=> Ans - (D)