Age of the universe is about 10¹⁰ years whereas the mankind has existed for 10⁶ years. For how many seconds would the man have existed if age of universe were 1 day?

The correct option is 8.64 s.

To find the equivalent duration for which mankind would have existed if the age of the universe were scaled to 1 day, we can use the concept of ratios. We compare the duration of mankind's existence to the total age of the universe, and then apply this same ratio to the scaled timeframe of 1 day.

Step 1: Calculate the ratio of mankind's existence to the age of the universe
The actual age of the universe is given as:

$$T_{\text{universe}}={10}^{10}\text{years}$$

The actual duration for which mankind has existed is:

$$T_{\text{mankind}}={10}^6\text{years}$$

The ratio of the mankind's existence to the age of the universe is:

$$\text{Ratio}=\frac{T_{\text{mankind}}}{T_{\text{universe}}}=\frac{{10}^6}{{10}^{10}}={10}^{-4}$$

Step 2: Convert the scaled age of the universe (1 day) into seconds
One day can be expressed in seconds as follows:

$$1\text{day}=24\text{hours}$$

$$1\text{day}=24\times 60\text{minutes}=1440\text{minutes}$$

$$1\text{day}=1440\times 60\text{seconds}=86400\text{seconds}$$

Step 3: Calculate the scaled existence of mankind
Using the ratio calculated in Step 1, we find the scaled existence time of mankind:

$$t_{\text{mankind}}=\text{Ratio}\times \text{Scaled age of universe}$$

$$t_{\text{mankind}}={10}^{-4}\times 86400\text{s}$$

$$t_{\text{mankind}}=8.64\text{s}$$

Thus, if the age of the universe were represented as 1 day, mankind would have existed for exactly 8.64 seconds.