The distance between two cities is 30 km. A man goes with 30 km speed per hour and returns with 20 km. speed per hour. What is his average speed?

Options

A. 25 km./hr
B. 24 km./hr
C. 10 km./hr
D. 26 km./hr

Explanation

To find the average speed of a man who travels to two cities with different speeds, we can use the formula for average speed when the distance is the same in both directions. Here’s how to solve the problem step by step:

### Step 1: Identify the distances and speeds
- The distance between the two cities is 30 km.
- The speed going to the city is 30 km/h.
- The speed returning from the city is 20 km/h.

### Step 2: Use the average speed formula
When the distance is the same for both trips, the average speed can be calculated using the formula:
\[ \text{Average Speed} = \frac{2xy}{x + y} \]
where:
- \(x\) is the speed going (30 km/h),
- \(y\) is the speed returning (20 km/h).

### Step 3: Substitute the values into the formula
Substituting the values into the formula gives:
\[ \text{Average Speed} = \frac{2 \times 30 \times 20}{30 + 20} \]

### Step 4: Calculate the numerator
Calculating the numerator:
\[ 2 \times 30 \times 20 = 1200 \]

### Step 5: Calculate the denominator
Calculating the denominator:
\[ 30 + 20 = 50 \]

### Step 6: Divide the numerator by the denominator
Now, we can find the average speed:
\[ \text{Average Speed} = \frac{1200}{50} = 24 \text{ km/h} \]

### Final Answer
The average speed of the man for the entire journey is **24 km/h**.

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