Auto-ignition time refers to the time it takes for a fuel-air mixture to ignite spontaneously without the need for an external ignition source. The ratio of fuel to air in the mixture plays a crucial role in determining the auto-ignition time.

The chemically correct fuel-air ratio, also known as the stoichiometric ratio, is the ideal ratio at which all the fuel is completely combusted with the available oxygen in the air. For petrol, this ratio is typically around 14.7:1, meaning that for every 14.7 parts of air, 1 part of fuel is required for complete combustion.

When the actual fuel-air ratio is lower than the chemically correct ratio, it means that there is an excess of air compared to the amount of fuel. On the other hand, when the actual fuel-air ratio is higher than the chemically correct ratio, it indicates that there is a surplus of fuel relative to the available air.

In the context of the given question, the auto-ignition time is minimum when the actual fuel-air ratio is 1.2 times the chemically correct ratio. This means that there is a slightly higher amount of fuel in the mixture compared to the ideal stoichiometric ratio.

This can be explained by the fact that a slightly richer mixture, with a higher fuel content, tends to ignite more easily and quickly compared to a lean mixture (lower fuel content). This is because the presence of excess fuel provides more combustible material, increasing the chances of ignition.

On the other hand, an excessively rich mixture with a significantly higher fuel content than the chemically correct ratio may lead to incomplete combustion and the formation of pollutants such as carbon monoxide (CO) and unburned hydrocarbons.

In summary, the auto-ignition time for a petrol-air mixture is minimum when the actual fuel-air ratio is slightly richer than the chemically correct ratio. This allows for easier and quicker ignition while maintaining efficient combustion.