Cat and Rat puzzle

A number of cats got together and decided to kill 999919 rats. Every cat killed an equal number of rats. Each cat killed more rats than there were cats. How many rats do you think each cat killed?

Cat and rat puzzle

Solution:

Answer: 1009 rats

Explanation: Total number of rats = 999919, (999919 = 1000000 – 81) = (1000² – 9² )

Using a² – b² = (a + b) (a – b)

= (1000 + 9) ( 1000 – 9)
= 1009 * 991

Here, each cat killed more rats than there were cats. Therefore, 991 cats killed 1009 rats each.