Merger of Two Partnership firm is NOT A RIGHT QUESTION. In my opinion it is something which is not possible.
See companies can be merged because they have a Separate Legal Entity which are different from the person who is the owner of it. Owner may change or come and go but company will remain the same. Now when Two companies are merged then the shares of both the companies are dissolved into New company and Old shareholders get the shares of New company.
But in partnership firm The firm has no separate legal entity different from it's owner and therefore it is not something which can be merged.
Rather it can be said that one firm has purchased the other OR say the PARTNERS of Two firms have joined together and form a new company OR Both the firms has been purchased by any company etc.
In case of Firm sold its business to Other Entity then Tax provisions of SLUMP SALE u/s 50B shall be applicable.