Thomas' formula uses:

positive tubes x 100 / sqrt(ml in negative tubes x ml in all tubes)

positive tubes / negative tubes

negative tubes x 100 / sqrt(ml in positive)

positive tubes x 100 x ml in all tubes

2078 Kartik · 4 marks

MPN per 100 ml numerical

Short answer

Using Thomas' formula: MPN/100 mL = (number of positive tubes × 100) / √[(mL in negative tubes) × (mL in all tubes)]. Total positive = 9, negative volume = 3.246, all volume = 6.666, so MPN = 900 / √(3.246×6.666) = 193.5 ≈ 193 per 100 mL.

What will be the MPN/100 ml, if 6 tubes for each diluted samples of 1.0 ml, 0.1 ml, 0.01 ml and 0.001 ml are taken and the no. of positive tubes are found to be 3, 4, 2 and 0 respectively in a multiple tube fermentation technique of coliform analysis?

Use Thomas' formula for the Most Probable Number:

\text{MPN}/100\ \text{ml} = \frac{\text{No. of positive tubes}\times100}{\sqrt{(\text{ml of sample in negative tubes})\times(\text{ml of sample in all tubes})}}

Dilution (ml)	Tubes	Positive	Negative	ml in negative tubes	ml in all tubes
1.0	6	3	3	3.000	6.000
0.1	6	4	2	0.200	0.600
0.01	6	2	4	0.040	0.060
0.001	6	0	6	0.006	0.006
Total		9		3.246	6.666

\text{MPN}/100\ \text{ml} = \frac{9\times100}{\sqrt{3.246\times6.666}} = \frac{900}{4.652} = 193.5

Answer: MPN $\approx 193$ per 100 ml.

✓ Answer checked by Claude Opus 5.5 (high effort)

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