The principle used in the pressure cooker is that the boiling point of water increases with an increase in pressure. Hence option (a) is the correct answer.
Pressure cooker has a confined space sealed from all side (except valve which is used to release excess pressure). When heat is supplied to the cooker it first increases the temperature of the water. When the temperature of the water reaches 100 degrees Celsius (water’s boiling point at atmospheric pressure) some of it starts converting to steam and starts filing the confined pressure cooker space.
Since steam is gaseous, it takes more space than water and covers all the vacant space insider cooker. With further heating, it reaches a point where there is no more space for the gaseous steam in the cooker and due to confined volume/space in the cooker, it gets compressed.
This compression increases the pressure inside the cooker to more than atmospheric pressure which in turn increases the boiling point of the remaining water (as the boiling point of water increases with increasing pressure).
Now the water which could go only up to 100 degrees Celsius under atmospheric pressure, goes beyond 100 degrees Celsius. Higher temperature of water means higher transfer of heat to food kept in it and hence the faster cooking.