Three persons cover a certain distance at a speed of 12 kmph, 15 kmph and 20 kmph respectively. Find their average speed.

Options

A. 15 km/hrs
B. 16 km/hrs
C. 12 km/hrs
D. 20 km/hrs

Answer

To find the average speed of three persons covering a certain distance at different speeds, we can use the formula for average speed when the distances are the same:

**Average Speed (V_avg) = (3 * S1 * S2 * S3) / (S1 * S2 + S2 * S3 + S3 * S1)**

Where:
- S1 = speed of the first person = 12 km/h
- S2 = speed of the second person = 15 km/h
- S3 = speed of the third person = 20 km/h

### Step-by-Step Solution:

1. **Identify the speeds**:
- S1 = 12 km/h
- S2 = 15 km/h
- S3 = 20 km/h

**Hint**: Make sure you clearly identify the speeds of all individuals involved.

2. **Calculate the product of the speeds**:
- Calculate \( S1 \times S2 \times S3 = 12 \times 15 \times 20 \).

\[ 12 \times 15 = 180 \]
\[ 180 \times 20 = 3600 \]

**Hint**: Multiply the speeds step by step to avoid confusion.

3. **Calculate the sum of the products of the speeds taken two at a time**:
- Calculate \( S1 \times S2 + S2 \times S3 + S3 \times S1 \).

\[ S1 \times S2 = 12 \times 15 = 180 \]
\[ S2 \times S3 = 15 \times 20 = 300 \]
\[ S3 \times S1 = 20 \times 12 = 240 \]

Now sum them up:
\[ 180 + 300 + 240 = 720 \]

**Hint**: Ensure you calculate each product correctly before summing them.

4. **Substitute the values into the average speed formula**:
\[ V_{avg} = \frac{3 \times 3600}{720} \]

5. **Calculate the average speed**:
- First, calculate \( 3 \times 3600 = 10800 \).
- Then divide by 720:
\[ V_{avg} = \frac{10800}{720} = 15 \text{ km/h} \]

**Hint**: Perform the division carefully to get the correct average speed.

### Final Answer:
The average speed of the three persons is **15 km/h**.