A bus goes from A to B at the rate of 30 kmph and from B to A at the rate of 60 kmph. The average speed of the bus is-

Options

A. 40 kmph
B. 45 kmph
C. `47cdot5` kmph
D. `52cdot5` kmph

Answer

To find the average speed of the bus when it travels from A to B and back from B to A, we can use the formula for average speed when the distances are the same. Here are the steps to solve the problem:

### Step 1: Identify the speeds
The bus travels from A to B at a speed of 30 km/h and from B to A at a speed of 60 km/h.

### Step 2: Use the formula for average speed
When the distances are the same, the average speed can be calculated using the formula:
\[ \text{Average Speed} = \frac{2 \times S_1 \times S_2}{S_1 + S_2} \]
where \(S_1\) is the speed from A to B (30 km/h) and \(S_2\) is the speed from B to A (60 km/h).

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ \text{Average Speed} = \frac{2 \times 30 \times 60}{30 + 60} \]

### Step 4: Calculate the denominator
Calculate the sum of the speeds:
\[ 30 + 60 = 90 \]

### Step 5: Calculate the numerator
Calculate the product in the numerator:
\[ 2 \times 30 \times 60 = 3600 \]

### Step 6: Divide the numerator by the denominator
Now, divide the numerator by the denominator to find the average speed:
\[ \text{Average Speed} = \frac{3600}{90} = 40 \text{ km/h} \]

### Final Answer
The average speed of the bus is **40 km/h**.

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