In a circus there was a leopard and a tiger walking in the two different rings of the same radii . There I observed that when leopard moved 3 steps tiger moves 5 steps in the same time but the distance travelled by leopard in 5 steps equal to the distance travelled by tiger in 4 steps . What is the number of round that a leopard made when tiger completed 100 rounds?

Options

A. 120
B. 48
C. 75
D. none of these

Answer

To solve the problem, we need to analyze the movements of the leopard and the tiger based on the information provided. Let's break it down step by step.

### Step 1: Understand the given information
- When the leopard moves 3 steps, the tiger moves 5 steps in the same amount of time.
- The distance the leopard travels in 5 steps is equal to the distance the tiger travels in 4 steps.

### Step 2: Set up the ratios
From the first piece of information, we can establish a ratio of the steps taken:
- Leopard's steps: 3
- Tiger's steps: 5

This gives us the ratio of their speeds as:
\[ \text{Speed of Leopard} : \text{Speed of Tiger} = 3 : 5 \]

From the second piece of information, we can establish another ratio based on the distances traveled:
Let the distance covered in one step by the leopard be \(d_L\) and by the tiger be \(d_T\). According to the information:
\[ 5d_L = 4d_T \]
This can be rearranged to find the ratio of distances:
\[ \frac{d_L}{d_T} = \frac{4}{5} \]

### Step 3: Calculate the effective speed ratio
Now, we can combine the two ratios to find the overall speed ratio. The speed of an animal can be defined as the product of the number of steps and the distance per step:
- Speed of Leopard = \(3 \times d_L\)
- Speed of Tiger = \(5 \times d_T\)

Using the distance ratio:
\[ d_L = \frac{4}{5}d_T \]

Substituting \(d_L\) in the speed of the leopard:
\[ \text{Speed of Leopard} = 3 \times \frac{4}{5}d_T = \frac{12}{5}d_T \]

Now, we can find the ratio of their speeds:
\[ \text{Speed of Leopard} : \text{Speed of Tiger} = \frac{12}{5}d_T : 5d_T = 12 : 25 \]

### Step 4: Determine the number of rounds
Let \(L\) be the number of rounds made by the leopard when the tiger completes 100 rounds. The ratio of the rounds made will be the same as the ratio of their speeds:
\[ \frac{L}{100} = \frac{12}{25} \]

### Step 5: Solve for \(L\)
Cross-multiplying gives:
\[ 25L = 1200 \]
\[ L = \frac{1200}{25} = 48 \]

### Conclusion
Thus, when the tiger completes 100 rounds, the leopard makes 48 rounds.

### Final Answer
The number of rounds that the leopard made when the tiger completed 100 rounds is **48**.

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