If the average life of a person is taken as 100 s the age of the universe on this scale is of the order

Options

A. `10^(10)s`
B. `10^(8)s`
C. `10^(17)s`
D. `10^(9)s`

Answer

To solve the problem of finding the age of the universe when the average life of a person is taken as 100 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Average Lifespan of a Person:**
The average lifespan of a person is given as 100 seconds in this scenario.

2. **Identify the Average Age of the Universe:**
The average age of the universe is typically estimated to be around \(10^{10}\) years. We need to convert this into seconds for consistency.

\[ \text{Age of the universe in seconds} = 10^{10} \text{ years} \times 365 \text{ days/year} \times 24 \text{ hours/day} \times 3600 \text{ seconds/hour} \]

\[ = 10^{10} \times 3.156 \times 10^7 \text{ seconds/year} \approx 3.156 \times 10^{17} \text{ seconds} \]

3. **Set Up the Ratio:**
Let \( AU \) be the average age of the universe and \( AP \) be the average age of a person. The ratio of the average age of the universe to the average age of a person is constant.

\[ \frac{AU}{AP} = \frac{3.156 \times 10^{17} \text{ seconds}}{10^{9} \text{ seconds}} = 3.156 \times 10^{8} \]

4. **Use the New Average Age of a Person:**
Now, we need to find the age of the universe \( AU' \) when the average age of a person \( AP' \) is 100 seconds.

\[ \frac{AU'}{AP'} = 3.156 \times 10^{8} \]

Substituting \( AP' = 100 \text{ seconds} \):

\[ AU' = 3.156 \times 10^{8} \times 100 \text{ seconds} \]

\[ AU' = 3.156 \times 10^{10} \text{ seconds} \]

5. **Final Result:**
The age of the universe on the scale where the average life of a person is taken as 100 seconds is approximately \( 3.156 \times 10^{10} \) seconds.

### Conclusion:
Thus, the age of the universe on this scale is of the order of \( 10^{10} \) seconds.

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