Question: Is this sentence correct? I recently read it in
an article:

"How does younger generation spend their money."

I want to know whether the usage of "their" in the above is correct

Answer: 
Collective nouns such as 'audience', 'team', or 'committee' can take singular or plural verbs depending on the notional reference in the speaker's or writer's mind.

In this case, the reference, judging by the verb, is to 'members of the younger generation', which makes sense. 

Quirk, Leech et al give a potentially ambiguous example, 'the audience were large' as potentially meaning a large number of people, or a number of large people, and suggest maintaining concord in writing, admitting a more relaxed use in practice when it comes to speech.
I think most people in the UK would say 'how the younger generation spends its money'.

'Their' might imply someone else's money e.g. their parents. 

And yes, as Leon points out 'the audience were large' suggests to me they were large people. The audience 'was large' means there were many of them.