Question

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?

• A. \(36\)
• B. \(75\)
• C. \(48\)
• D. \(100\)

Hint:

Speed ratio can be simplified as: \((\text{Steps}_1 \times \text{Inverse Steps for equal distance}_1) : (\text{Steps}_2 \times \text{Inverse Steps for equal distance}_2)\).
Here: \((3 \times 4) : (5 \times 5) = 12 : 25\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Since both rings have the same radii, their circumferences are identical. The ratio of rounds completed in the same time will be the same as the ratio of their speeds (distance covered in the same time).
Step 2: Key Formula or Approach:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\text{Number of steps} \times \text{Length of each step}}{\text{Time}} \] Step 3: Detailed Explanation:
1. Let the length of one step of the Leopard be \(L\) and one step of the Tiger be \(T\).
2. Given: Distance in \(5\) steps of Leopard = Distance in \(4\) steps of Tiger.
\[ 5L = 4T \implies L = \frac{4}{5}T \] 3. In the same time \(t\), Leopard takes \(3\) steps and Tiger takes \(5\) steps.
Distance covered by Leopard (\(D_L\)) = \(3 \times L = 3 \times (\frac{4}{5}T) = \frac{12}{5}T\).
Distance covered by Tiger (\(D_T\)) = \(5 \times T = 5T\).
4. Ratio of their speeds (Distances in time \(t\)):
\[ \frac{V_L}{V_T} = \frac{(12/5)T}{5T} = \frac{12}{25} \] 5. Ratio of rounds completed:
\[ \frac{\text{Rounds of Leopard}}{\text{Rounds of Tiger}} = \frac{12}{25} \] \[ \text{Rounds of Leopard} = \frac{12}{25} \times 100 = 4 \times 12 = 48 \] Step 4: Final Answer:
The leopard completed \(48\) rounds.