A man travelled from A to B at a speed of 10 m/sec, and returned to A from B at a speed of x km/h. If his average speed is 45 km/h, then what is the value of x ?

Options

A. 54
B. 50
C. 56
D. 60

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript:

### Step 1: Convert the speed from m/sec to km/h
The speed of the man from A to B is given as 10 m/sec. To convert this to km/h, we use the conversion factor where 1 m/sec is equal to 18/5 km/h.

\[ S_1 = 10 \, \text{m/sec} \times \frac{18}{5} = 36 \, \text{km/h} \]

### Step 2: Define the average speed formula
The average speed \( V_{avg} \) for a round trip can be calculated using the formula:

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

Where:
- \( S_1 \) is the speed from A to B (36 km/h)
- \( S_2 \) is the speed from B to A (x km/h)

Given that the average speed is 45 km/h, we can set up the equation:

\[ 45 = \frac{2 \times 36 \times x}{36 + x} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives:

\[ 45(36 + x) = 2 \times 36 \times x \]

### Step 4: Expand and simplify the equation
Expanding both sides:

\[ 1620 + 45x = 72x \]

### Step 5: Rearrange the equation to solve for x
Rearranging gives:

\[ 1620 = 72x - 45x \]
\[ 1620 = 27x \]

### Step 6: Solve for x
Dividing both sides by 27:

\[ x = \frac{1620}{27} = 60 \, \text{km/h} \]

### Conclusion
The value of \( x \) is 60 km/h.

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