A person goes from point L to N and comes back. His average speed for the whole journey is 100 km/hr. If his speed while coming back from N to L is 65 km/hr, then what will be the speed of the person (in km/hr) while going from L to N?

Options

A. a)135
B. b)`146.31`
C. c)`150.62`
D. d)`216.67`

Answer

To find the speed of the person while going from point L to N, we can use the formula for average speed when the distances are equal. The average speed \( V_{avg} \) for a round trip can be calculated using the formula:

\[ V_{avg} = \frac{2 \cdot S_1 \cdot S_2}{S_1 + S_2} \]

Where:
- \( S_1 \) is the speed from L to N (which we need to find, let's denote it as \( x \)).
- \( S_2 \) is the speed from N to L, which is given as 65 km/hr.
- \( V_{avg} \) is the average speed for the whole journey, which is given as 100 km/hr.

### Step 1: Set up the equation using the average speed formula
Substituting the known values into the formula:

\[ 100 = \frac{2 \cdot x \cdot 65}{x + 65} \]

### Step 2: Cross-multiply to eliminate the fraction
Cross-multiplying gives:

\[ 100(x + 65) = 130x \]

### Step 3: Expand the left side
Expanding the left side:

\[ 100x + 6500 = 130x \]

### Step 4: Rearrange the equation
Rearranging the equation to isolate \( x \):

\[ 6500 = 130x - 100x \]
\[ 6500 = 30x \]

### Step 5: Solve for \( x \)
Now, divide both sides by 30 to find \( x \):

\[ x = \frac{6500}{30} = \frac{650}{3} \approx 216.67 \text{ km/hr} \]

### Conclusion
The speed of the person while going from L to N is approximately \( 216.67 \) km/hr.