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 find the ratio of the output power of the first man to the second man. Let's break it down step by step.

### Step 1: Understand the concept of power
Power is defined as the rate at which work is done. It can be mathematically expressed as:
\[ P = \frac{W}{t} \]
where \( P \) is power, \( W \) is work done, and \( t \) is the time taken to do that work.

### Step 2: Calculate the power of the first man
Let’s denote the work done by both men as \( W \). The first man does this work in 10 seconds. Therefore, the power \( P_1 \) of the first man can be calculated as:
\[ P_1 = \frac{W}{10} \]

### Step 3: Calculate the power of the second man
The second man does the same amount of work \( W \) but takes 20 seconds to do it. Thus, the power \( P_2 \) of the second man is:
\[ P_2 = \frac{W}{20} \]

### Step 4: Find the ratio of the powers
Now, we need to find the ratio of the power of the first man to the power of the second man:
\[ \frac{P_1}{P_2} = \frac{\frac{W}{10}}{\frac{W}{20}} \]

### Step 5: Simplify the ratio
When we simplify the ratio, the work \( W \) cancels out:
\[ \frac{P_1}{P_2} = \frac{W}{10} \times \frac{20}{W} = \frac{20}{10} = 2 \]

### Step 6: Conclusion
Thus, the ratio of the output power of the first man to the second man is:
\[ \frac{P_1}{P_2} = 2:1 \]

### Final Answer
The ratio of the output power of the first man to the second man is \( 2:1 \).

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