In circus there was a leopard and a tiger walking in the two different rings…

Concept: When two bodies move on circular tracks of equal radius, the circumference each must cover per round is the same. So, for a given time period, the number of rounds each completes is directly proportional to its speed (rounds ∝ distance covered ∝ speed, since time is common). Speed itself equals the rate at which steps are taken multiplied by the length of each step: speed = (steps per unit time) × (length per step).

1. Step-rate ratio: the leopard takes 3 steps while the tiger takes 5 steps in the same time, so (leopard step-rate) : (tiger step-rate) = 3 : 5.

2. Stride-length ratio: the distance covered in 5 leopard steps equals the distance covered in 4 tiger steps, so 5 × (leopard stride) = 4 × (tiger stride), giving (leopard stride) : (tiger stride) = 4 : 5.

3. Speed ratio: since speed = step-rate × stride-length, (leopard speed) : (tiger speed) = (3 × 4) : (5 × 5) = 12 : 25.

4. Because both rings have the same radius, rounds completed in the same overall time are proportional to speed, so (leopard rounds) : (tiger rounds) = 12 : 25.

5. Given the tiger completes 100 rounds, the leopard completes 100 × 12/25 = 48 rounds.

Cross-check: let the tiger's stride be 5 units, so the leopard's stride is 4 units (matching the 4 : 5 stride ratio). In one common time unit, the leopard takes 3 steps, covering 3 × 4 = 12 units, while the tiger takes 5 steps, covering 5 × 5 = 25 units. The distance ratio 12 : 25 matches the speed ratio derived above, confirming the combination — the leopard makes 48 rounds when the tiger makes 100.