If two samples are different in size, like 20 to 60, is it a good idea to apply two sample t-tests and chi-square tests?

It’s been quite a few years since I was at uni and I have effectively forgotten everything I ever knew about statistics. So here I am.

All other prerequisites for the two sample t- test (for the continuous variables) and the chi square test (for the categorical ones) are valid. The two samples are independent, normal distribution etc etc. The only problem is that according to my old statistics book, the two samples that are to be compared need to be “equal in size”. There is no hint whatsoever about how much different in size the two samples can be.
Should I downsize the big sample to n=20 (option A) or should I go on and apply the tests (option B)? What are the pros and cons when going with option A and what when going with option B?

I am pretty sure I am going to lose on statistical power either way, but I am not sure which of the two options is the most acceptable.