From a bus terminal, buses starts at on interval of 24 min. If a man goes away from bus terminal and meet bus at an interval of 28 min. If speed of man is 5 km/hr, then find the speed of bus.

Options

A. 25 km
B. 75 km
C. 50 km
D. 35 km

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Problem
We have two entities: a bus and a man. The bus leaves the terminal every 24 minutes, and the man meets the bus after 28 minutes. The speed of the man is given as 5 km/hr. We need to find the speed of the bus.

### Step 2: Identify the Time Difference
The bus takes 24 minutes to leave the terminal, and the man meets the bus after 28 minutes. The difference in time is:
\[ \text{Time taken by bus} = 24 \text{ minutes} \]
\[ \text{Time taken by man} = 28 \text{ minutes} \]
The difference in time is:
\[ 28 \text{ minutes} - 24 \text{ minutes} = 4 \text{ minutes} \]

### Step 3: Set Up the Ratio of Times
The time taken by the bus to travel a certain distance is 4 minutes, while the man takes 28 minutes to cover the same distance. Therefore, the ratio of the time taken by the bus to the time taken by the man is:
\[ \text{Bus time : Man time} = 4 : 28 = 1 : 7 \]

### Step 4: Inverse Relationship Between Speed and Time
Since speed and time are inversely related, we can take the inverse of the time ratio to find the speed ratio:
\[ \text{Speed of Man : Speed of Bus} = 7 : 1 \]

### Step 5: Use the Speed of the Man
We know the speed of the man is 5 km/hr. Let the speed of the bus be \( x \) km/hr. According to the ratio:
\[ \frac{5}{x} = \frac{7}{1} \]

### Step 6: Solve for the Speed of the Bus
Cross-multiplying gives:
\[ 5 \cdot 1 = 7 \cdot x \]
\[ 5 = 7x \]
Now, solving for \( x \):
\[ x = \frac{5}{7} \text{ km/hr} \]

### Step 7: Convert the Speed to km/hr
To find the speed of the bus, we can rearrange the equation:
\[ x = 5 \cdot \frac{1}{7} \]
Calculating this gives:
\[ x = 35 \text{ km/hr} \]

### Final Answer
The speed of the bus is **35 km/hr**.

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