As per section 44AB, any assessee "carrying on business shall, if his total sales, turnover or gross receipts, as the case may be, in business exceed or exceeds one crore rupees in any previous year;"
Tax audit will be applicable on a partnership firm business if the gross turnover/receipts in the PY exceed 1 Cr. Thus, audit is not mandatory in the above case where turnover is Rs 603484.
Don't confuse this with section 44AD, talking about presumptive taxation.
Earlier Section 44AD, Subsection (5) read as follows:
"(5) Notwithstanding anything contained in the foregoing provisions of this section, an eligible assessee who claims that his profits and gains from the eligible business are lower than the profits and gains specified in sub-section (1) and whose total income exceeds the maximum amount which is not chargeable to income-tax, shall be required to keep and maintain such books of account and other documents as required under sub-section (2) of section 44AA and get them audited and furnish a report of such audit as required under section 44AB"
which implies, that any assessee who is eligible u/s 44AD (includes a resident partnership firm in your case) which declares profits/gains less than 8% of turnover (as deemed to be calculated under subsection 1 ) has to maintain BOA & get it's accounts audited.
With the amendement by Finance Act, 2016, w.e.f. 1-4-2017 law reads as follows :
"(5) Notwithstanding anything contained in the foregoing provisions of this section, an eligible assessee to whom the provisions of sub-section (4) are applicable and whose total income exceeds the maximum amount which is not chargeable to income-tax, shall be required to keep and maintain such books of account and other documents as required under sub-section (2) of section 44AA and get them audited and furnish a report of such audit as required under section 44AB."
"(4) Where an eligible assessee declares profit for any previous year in accordance with the provisions of this section and he declares profit for any of the five assessment years relevant to the previous year succeeding such previous year not in accordance with the provisions of sub-section (1), he shall not be eligible to claim the benefit of the provisions of this section for five assessment years subsequent to the assessment year relevant to the previous year in which the profit has not been declared in accordance with the provisions of sub-section (1)"
Which implies, that maintenance of BOA & audit of same is mandatory required is sub-section (4) is attracted & Total income > taxable limit.
Subsection (4) is attracted when an assessee who declares profit under Presumptive taxation scheme in any PY , declares profit for any subsequent 5 AY's for amount less than 8% of turnover (received in bank/cheque mode) and 6% (received in cash mode), he cannot opt for Presumptive taxation scheme for next 5 AY's and has to maintain BOA & get accounts audited ( ignoring the slabs as given u/s 44AA & 44AD )
Basically, if you've opted for presumptive taxation scheme & claimed profit < 8%/6% of turnover in any PY but has not followed the same continuously for the next 5 years i.e., before completion of 6 years has declared lower profits, he cannot avail benefit of the sceme for next 5 years & has to mandatorily maintain BOA & get accounts audited despite the slab applicability of tax audit