A man does a given amount of work in 10 sec. Another man does the same amount of work in 20 sec. The ratio of the output power of first man to the second man is

Options

A. 1
B. `(1)/(2)`
C. `(2)/(1)`
D. none of these

Explanation

To solve the problem, we need to calculate the output power of both men and then find the ratio of their powers.

### Step 1: Define the formula for output power
Output power (P) is defined as the work done (W) divided by the time taken (t). The formula is:
\[ P = \frac{W}{t} \]

### Step 2: Calculate the output power of the first man
Let’s denote the work done by both men as W (same amount of work). The first man does this work in 10 seconds. Therefore, his output power (OP1) can be calculated as:
\[ OP1 = \frac{W}{10} \]

### Step 3: Calculate the output power of the second man
The second man does the same amount of work W in 20 seconds. Therefore, his output power (OP2) can be calculated as:
\[ OP2 = \frac{W}{20} \]

### Step 4: Find the ratio of the output power of the first man to the second man
Now, we can find the ratio of the output power of the first man to that of the second man:
\[ \text{Ratio} = \frac{OP1}{OP2} = \frac{\frac{W}{10}}{\frac{W}{20}} \]

### Step 5: Simplify the ratio
When we simplify the ratio, we can cancel W:
\[ \text{Ratio} = \frac{1/10}{1/20} = \frac{20}{10} = 2 \]

### Final Result
Thus, the ratio of the output power of the first man to the second man is:
\[ 2:1 \]