A person goes from point N to P and comes back. His average speed for the whole journey is 60km/hr. If his speed while going from N to P is 40 km/hr, then what will be the speed of the person (in km/hr) while coming back from P to N?

Options

A. 90
B. 100
C. 120
D. 140

Answer

To solve the problem, we need to find the speed of the person while coming back from point P to point N, given that the average speed for the entire journey is 60 km/hr and the speed while going from N to P is 40 km/hr.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Average speed for the whole journey (N to P and back to N) = 60 km/hr.
- Speed from N to P = 40 km/hr.
- Let the speed from P to N be denoted as \( y \) km/hr.

2. **Use the Formula for Average Speed:**
The formula for average speed when the distance is the same in both directions is given by:
\[ \text{Average Speed} = \frac{2xy}{x + y} \]
where \( x \) is the speed from N to P and \( y \) is the speed from P to N.

3. **Substitute the Known Values:**
Substitute \( x = 40 \) km/hr and the average speed = 60 km/hr into the formula:
\[ 60 = \frac{2 \cdot 40 \cdot y}{40 + y} \]

4. **Simplify the Equation:**
- Multiply both sides by \( (40 + y) \):
\[ 60(40 + y) = 80y \]
- Distribute the 60:
\[ 2400 + 60y = 80y \]

5. **Rearrange the Equation:**
- Move all terms involving \( y \) to one side:
\[ 2400 = 80y - 60y \]
- This simplifies to:
\[ 2400 = 20y \]

6. **Solve for \( y \):**
- Divide both sides by 20:
\[ y = \frac{2400}{20} = 120 \text{ km/hr} \]

### Final Answer:
The speed of the person while coming back from P to N is **120 km/hr**.