Cat and dog had a competition over who is faster. cat’s jump is 5% shorter, but it makes 5% more jumps than dog does in the same time. who will win the competition?

Let's say the dog jumps 100 feet every jump, (Yes, I know that it's illogical, but it makes this problem so much easier.) and that it jumps 1 time every second.
100 · 1 = 100, so Dog goes at 100 feet per second.

Cat jumps 5% shorter, so it is 95 feet per jump. However, it jumps 5% more than dog, so it jumps 1.05 times every second. You multiply.
95 · 1.05 = 99.75. So Cat goes at 99.75 feet per second.

100 > 99.75

Dog is going to win the race.