Q.71 One-ml sample of a bacterial culture was serially diluted to 𝟏𝟎^𝟓 times, and 46 colonies were obtained
after plating this diluted sample on an agar medium. The number of cells present per ml in the undiluted
original sample were ____

Calculate Bacterial Cell Count from Serial Dilution

The number of cells per ml in the undiluted original sample is
4.6 × 10⁶. This bacterial culture dilution problem uses the
standard plate count method, where colonies represent viable cells adjusted
for dilution factor and plating volume.

Serial dilution to 10⁵ reduces cell density, and plating
1 ml (standard assumption) of this dilution yields 46 colonies.

Problem Breakdown

Start with 1 ml of original culture diluted serially to
10⁵-fold, meaning the final dilution factor (DF) is
10⁵.

Each colony arises from one viable cell in the plated 1 ml sample, so the concentration
in the diluted sample equals 46 cells/ml.

Multiply by the dilution factor to back-calculate the original concentration:

(46 cells/ml) × 10⁵ = 4.6 × 10⁶ cells/ml

Step-by-Step Calculation

• Dilution factor: 10⁵ (100,000-fold dilution)
• Colonies counted: 46 (from 1 ml plated volume)
• Diluted concentration: 46 CFU/ml
• Original concentration:
  46 × 10⁵ = 4,600,000 =
  4.6 × 10⁶ cells/ml

This assumes plating the entire 1 ml diluted sample, which is common in microbiology
protocols where colony counts between 30–300 are considered ideal.

Common Mistakes Explained

Students often confuse plating volume or forget dilution adjustment. For example, if
0.1 ml were plated instead:

46 colonies × 10 = 460 CFU/ml (diluted sample)

Original concentration = 460 × 10⁴ =
4.6 × 10⁶ cells/ml

Typical MCQ trap options include:

• 46 cells/ml (ignores dilution factor)
• 46 × 10⁵ without scientific notation clarity
• 46 ÷ 10⁵ (wrong direction of dilution)

The correct answer consistently aligns with
4.6 × 10⁶ cells/ml.

Key Formula Reference

CFU/ml (original) = (Number of colonies ÷ Plated volume in ml) × Dilution factor

In this case, plated volume = 1 ml, so the formula simplifies to:

CFU/ml = Colonies × Dilution Factor