What methods are being used to solve the problem?

[Kumarc]

What methods are being used to solve the problem?
What methods are used to solve the problem?

Which one is correct? Can we use them in different tenses according to grammar?

 

[tedmc]

Both are possible. The difference is in the time of the actions.
The first question refers to methods being used to solve an on-going problem, while the second is a question about methods currently being used in general.