I have the feeling that the answer to this question depends on whether the writer regards the plural noun - people - as a group or as a number of unrelated individuals. A group of people need motorbikes for commuting. But a number of unrelated individuals need, each one, only one motorbike for commuting.Do I say ? Many people world need a motorbike or motorbikes for commuting in the city nowadays..
I've revised my view; I think I was looking at the wrong end of the equation. Here's my new take: The indefinite article a does not always have the meaning of 'one'. When we say, A doctor must like people, we're not saying, One doctor must like people. Instead, we are using a to introduce a kind of profession - or as the grammar says - "a member of a class," i.e. a doctor is a member of a class (category) called professions. In the sentence Many people need a motorbike for commuting, we are not using a with the meaning of 'one'; we use it to introduce a member, motorbike, of a class called vehicles.But from this your technical thought, whatever mode you base on, still the 2 types of your sentecnes still mean the same things or different meaning?