GATE 2026 BT Q.33: solution and answer

Official answer: 40000Source: Official answer key, GATE 2026 BT (IIT Guwahati)

1. Each colony grows from one viable cell, so the count of colony forming units (CFU) on the plate equals the number of viable cells in the volume plated. The viable count of the original culture is $\frac{\text{colonies}}{\text{volume plated}}\times \text{dilution factor}$.

2. Convert the plated volume to mL: $50\mu \text{L}=0.05\text{mL}$.

3. Concentration of the diluted sample: $\frac{20\text{CFU}}{0.05\text{mL}}=400{\text{CFU mL}}^{-1}$.

4. The sample was diluted 100-fold, so the original culture is 100 times more concentrated: $400\times 100=40000{\text{CFU mL}}^{-1}$.

5. The viable cell count of the culture is $4\times 10^4{\text{CFU mL}}^{-1}$, that is 40000 as an integer.