A hunter fired two shots from the branch of a tree at an interval of 76 seconds. A tiger separating too fast hears the two shots at an interval of 83 seconds. If the velocity of the sound is 1195.2 km/h, then find the speed of tiger?

Options

A. 112.8 km/h
B. 100.8 km/h
C. 80.16 km/h
D. none of these

Answer

To find the speed of the tiger, we can use the relationship between the speed of sound, the speed of the tiger, and the time intervals involved. Here’s a step-by-step solution:

### Step 1: Understand the given information
- The interval between the two shots fired by the hunter is 76 seconds.
- The interval at which the tiger hears the two shots is 83 seconds.
- The speed of sound is given as 1195.2 km/h.

### Step 2: Calculate the difference in time
The difference in time between when the tiger hears the two shots and when the shots were fired is:
\[ \text{Difference in time} = 83 \text{ seconds} - 76 \text{ seconds} = 7 \text{ seconds} \]

### Step 3: Set up the relationship
According to the problem, we can set up the relationship:
\[ \frac{\text{Speed of sound}}{\text{Speed of tiger}} = \frac{\text{Time taken}}{\text{Difference in time}} \]
Substituting the known values:
\[ \frac{1195.2 \text{ km/h}}{v} = \frac{83 \text{ seconds}}{7 \text{ seconds}} \]
Where \( v \) is the speed of the tiger.

### Step 4: Solve for the speed of the tiger
Cross-multiplying gives us:
\[ 1195.2 \text{ km/h} \cdot 7 = v \cdot 83 \]
This simplifies to:
\[ v = \frac{1195.2 \cdot 7}{83} \]

### Step 5: Calculate the value
Now, we can calculate the value:
\[ v = \frac{1195.2 \cdot 7}{83} = \frac{8366.4}{83} \approx 100.8 \text{ km/h} \]

### Final Answer
The speed of the tiger is approximately **100.8 km/h**.

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