Applying for different PhD positions in the same research group Suppose there is a research group X under the supervision of two professors. They put out an advertisement seeking 2 PhD students one for experimental research and one for theoretical/numerical work.

If a student has experience and necessary skills in both experimental and theoretical/numerical research of that particular field, is it ok for him to apply for both the positions?

And if he tailors his CV and motivation letter for the specific position he is applying(individual application has to be sent for each position) for, will it look good if the professors read the both application. Or will they think that the student is an imposter?

Given that the PhD positions are highly competitive, the student is ready to work on either experimental or computational. 

So, is it ok to apply for both the positions?
It is okay to apply to both positions.  The student might even be at an advantage, having interests and skills in both areas.  I might try to contact both professors in advance, and ask if they would like the application structured as one or two applications.  If the student does submit two applications, I would recommend stating in the cover letter that they are applying to both, and would be excited to work in either position.