In a circus, a leopard and a tiger walk in separate rings of the same radius. The leopard makes 3 steps while the tiger makes 5 in the same time. The distance of 5 leopard steps equals 4 tiger steps. When the tiger completes 100 rounds, how many rounds has the leopard completed?

Introduction / Context:
Number of rounds is proportional to linear speed for equal-ring circumference. Speed here equals steps per unit time times step length.

Given Data / Assumptions:

• Steps per equal time: leopard : tiger = 3 : 5.
• 5 leopard steps = 4 tiger steps → L_leopard / L_tiger = 4/5.
• Equal ring radius (equal circumference).

Concept / Approach:
v_leopard / v_tiger = (3/5) * (4/5) = 12/25. Rounds completed are in the same ratio as speeds over the same time.

Step-by-Step Solution:
Speed ratio = 12 : 25.If tiger makes 100 rounds, leopard makes 100 * (12/25) = 48 rounds.

Verification / Alternative check:
Compare distances per minute: scaling confirms leopard covers 48% of tiger's distance.

Why Other Options Are Wrong:
75 or 120 assume inverted or additive ratios; none match the combined frequency-length effect.

Common Pitfalls:
Using 5/4 instead of 4/5 for step lengths or adding the ratios rather than multiplying.

Final Answer:
48