In a circus there were a leopard and a tiger walking in the two different rings having same radii. It was observed that when leopard moved 3 steps, tiger moved 5 steps in the same time, but the distance traversed by leopard in 5 steps is equal to the distance traversed by tiger in 4 steps. How many rounds that a leopard made till when tiger completed 100 rounds?

Let the distance travelled by leopard in one step be $$x$$ units.

It is given, distance traversed by leopard in 5 steps is equal to the distance traversed by tiger in 4 steps

So, distance travelled by tiger in one step = $$\dfrac{5x}{4}$$ units.

Now, leopard moved 3 steps and tiger moved 5 steps in the same time.

So, in the same time, leopard is moving $$3\times\ x=3x$$ units.

And, distance travelled by the tiger = $$5\times\ \dfrac{5x}{4}=\dfrac{25x}{4}$$ units.

So, speed ratios of leopard and tiger

= $$\dfrac{3x}{\dfrac{25x}{4}}=\dfrac{12x}{25x}=\dfrac{12}{25}$$

So, number of rounds covered by leopard = $$\dfrac{12}{25}\times\ 100=48$$