Q.82. A bacterial culture containing 𝟑 × 𝟏𝟎^𝟓 live cells was exposed to a newly developed sterilizing
agent. After 30 minutes of exposure, 3 live cells remained in culture. The decimal reduction time (in
minutes) for the new agent is ____ .

Decimal reduction time (D-value) measures the time required to reduce a microbial population by 90% (one log cycle) under defined conditions.
In this GATE microbiology problem, a culture drops from
3 × 10⁵ cells to 3 cells in 30 minutes, yielding a
D-value of 6 minutes.

Problem Breakdown

Initial live cells:
N₀ = 3 × 10⁵
Final cells after 30 minutes:
N = 3

Microbial death follows first-order kinetics:

log₁₀(N₀/N) = t / D

where t is exposure time and D is the decimal reduction time.

Calculation Steps

1. Compute the Cell Ratio

N₀ / N = (3 × 10⁵) / 3 = 10⁵

2. Determine Log Reductions

log₁₀(10⁵) = 5

3. Calculate D-Value

D = t / log₁₀(N₀/N)

D = 30 / 5 = 6 minutes

This calculation assumes log-linear survival, which is standard for evaluating sterilizing agents.

Why Other Values Are Incorrect

Common distractors include:

• 30 minutes: Incorrect — represents total exposure time, not time per log reduction.
• ≈ 0 minutes: Incorrect — dividing time by total cells ignores first-order kinetics.
• 10 minutes: Incorrect — assumes a 10³ reduction, ignoring the actual
  10⁵ reduction from 3 × 10⁵ to 3 cells.

Only D = 6 minutes fits the exact log reduction observed.

Applications in Microbiology

D-values are critical for designing sterilization protocols in
food safety and pharmaceutical manufacturing.
Processes such as the 12D concept are used to eliminate pathogens like
Clostridium botulinum.

In this case, a 6-log reduction in 30 minutes demonstrates high sterilization efficacy.