GATE 2025 AG – Question 63
Cans contain .5 kg peas each and are processed at 121°C. One group starts with 5×10¹⁰ Clostridium spores/can;another with Bacillus spores. Desired spoilage probability is 5 cans per 100. Decimal reduction times are respectively 2.5 and 6.0 min. All cans receive the same lethality. Find initial Bacillus spores/g peas as an integer.
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Correct answer: 10 to 10
Explanation
Use the standard rare-survivor design approximation of .05 surviving spores per can. Clostridium needs $\log_{10}[(5\times10^{10})/.05]=12$ decimal reductions, so process time is $12(2.5)=30$ min. This gives Bacillus $30/6=5$ decimal reductions. Its allowed initial load is $.05(10^5)=5000$ spores/can. Divide by 500 g/can to obtain **10 spores/g**. Exact Poisson conversion of a 5% spoilage probability changes the intermediate survivor mean slightly but retains the integer answer.