SBI PO Prelims 4 Aug 2025 Shift 1 Paper

Concept:The problem uses the repeated replacement formula: final concentration equals initial concentration multiplied by $(1 - \frac{x}{V})^n$, where $x$ is the amount replaced each time, $V$ is the total volume, and $n$ is the number of replacements.Explanation:Initial milk volume is $80$ liters.Let $x$ liters of the mixture be removed and replaced with water each time.After the first replacement, milk left = $(80 - x)$ liters.The fraction of milk in the mixture becomes $\frac{80 - x}{80}$.After the second replacement, the same fraction of milk is removed again.Thus milk left after the second replacement = $\left(\frac{80 - x}{80}\right) \times (80 - x)= \frac{(80 - x)^2}{80}$.Hence the final concentration of milk = $\left(\frac{80 - x}{80}\right)^2$.Given final concentration = $96.04\% = 0.9604$.So $\left(\frac{80 - x}{80}\right)^2 = 0.9604$.Taking square root: $\frac{80 - x}{80} = \sqrt{0.9604} = 0.98$.Then $80 - x = 0.98 \times 80 = 78.4$.Therefore $x = 80 - 78.4 = 1.6$ liters.Answer:$1.6$ liters (Option B).