Circus Rings and Step Ratios

Let the distance traversed by leopard in 1 step be $x$ and tiger in 1 step be $y$. Given $5x = 4y \implies y = \frac{5}{4}x$.

In a given time:

• Leopard covers $3$ steps = $3x$
• Tiger covers $5$ steps = $5y = 5 \left(\frac{5}{4}x\right) = \frac{25}{4}x$

Ratio of speeds (or distance covered in same time): $\frac{\text{Leopard}}{\text{Tiger}} = \frac{3x}{\frac{25}{4}x} = \frac{12}{25}$

Number of rounds made by leopard when tiger completes 100 rounds: $= 100 \times \frac{12}{25} = 48$