A goes office at a speed of 10 km/hr and returns home at 40 km/hr. What is his average speed (in km/hr)?

Options

A. 16
B. 24
C. 25
D. 32

Answer

To find the average speed of A's journey to the office and back home, we can use the formula for average speed when the distances are the same but the speeds are different. The formula is:

\[ \text{Average Speed} = \frac{2xy}{x + y} \]

Where:
- \(x\) is the speed going to the office,
- \(y\) is the speed returning home.

### Step 1: Identify the speeds
- Speed going to the office (\(x\)) = 10 km/hr
- Speed returning home (\(y\)) = 40 km/hr

### Step 2: Substitute the values into the formula
Now, we can substitute the values of \(x\) and \(y\) into the average speed formula:

\[ \text{Average Speed} = \frac{2 \times 10 \times 40}{10 + 40} \]

### Step 3: Calculate the numerator
Calculating the numerator:

\[ 2 \times 10 \times 40 = 800 \]

### Step 4: Calculate the denominator
Calculating the denominator:

\[ 10 + 40 = 50 \]

### Step 5: Calculate the average speed
Now, we can calculate the average speed:

\[ \text{Average Speed} = \frac{800}{50} = 16 \text{ km/hr} \]

### Final Answer
The average speed of A's journey is **16 km/hr**.

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