blacks in my photoshop file saved as PDF appearing as gray to another user

Im currently working on a business card in photoshop under CMYK as its supposed to be printed

Technically, just because a file is to be printed, it doesn't have to be in CMYK mode. 

You have set a very safe 240% total ink coverage for a large area of solid black, which is a good thing to do. 

240% total ink obviously has less density than the extreme of 400% total ink, so a good PDF viewing application such as Acrobat will show the differences between the two. So yes, one may appear to be "grey" compared to the other, however, the "grey" one will still print and view as black if the CMYK values are honoured.

Having an ICC profile embedded in the PDF will inform an ICC colour-managed application of the intent of the CMYK numbers. Not all PDF viewers are colour-managed. Even if a PDF application is colour-managed, it may show slight differences between a PDF with and without an embedded ICC profile due to its colour management settings for assumed colour modes.

Here is a screenshot from Apple Preview on a Mac, the same 240% CMYK values as yours, but one PDF had an embedded ICC profile (left-hand side) and the other didn't (right-hand side):

In Photoshop, if one uses the View > Proof Colors feature for a CMYK profile with "Simulate Black Ink" activated, you will see a similar result, softproof on (left) and softproof off (right):

When viewing CMYK PDF files, one should use an appropriate PDF viewer, which is most often Adobe Acrobat Reader as an entry-point (there are other options, however, these come at a cost and are purpose-built for prepress, not consumers).

To add a few details , the black is 60,40,40,100 in CMYK