Why only type -Ia supernovae are used as standard candle to calculate age of universe and why not type II, type Ib, type 1c ?
A type 1a supernova forms when a white dwarf grows through accretion to a certain size, at which it becomes unstable. This means that the precursor object is always a white dwarf of mass 1.39 solar masses. As the precursor object is always of the same type and the same size, the supernova is thought to be the same brightness.
On the other hand, type II supernovae form from the collapse of giant stars. The precursor object can have a range of masses from about 10 Solar masses, to a maximum of over 100. The brightness of the supernova depends on the mass of the precursor (and other factors such as the metallicity) and so type II supernovae are not all equally bright.
The other types also have precursors which vary in size or other factors, only type 1a supernovae are thought to always have a white dwarf of mass 1.39 as a standard precursor, so only type 1a are suitable as a standard candle.