1
Most people didn’t want this type of jobs in the past.
Most people didn’t want this type of job in the past.
Most people didn’t want these types of jobs in the past.
With this or that, use singular type and a singular noun: ‘this type of job’, ‘that type of problem’.
With these or those, use plural types and, usually, a plural noun: ‘these types of jobs’, ‘those types of problems’.
2
We saw all type of animals.
We saw all types of animals.
I don’t like going to these type of places.
I don’t like going to this type of place.
I don’t like going to these types of places.
After plural words such as all, these, those, many and several, use plural types: ‘all types of animals’, ‘several types of cars’.