SBI PO Prelims 8 Mar 2025 Shift 2 Paper

Concept:Use the given ratio of total quantities to find the scale factor, then determine the initial composition by working backwards.Explanation:Let initial total mixture be $15x$ liters and final mixture be $11x$ liters.Net change in total quantity = removal of 28 L minus addition of 16 L = $-12$ L.Thus, $11x = 15x - 12$ implies $4x = 12$, so $x = 3$.Initial total = $15 \times 3 = 45$ L, final total = $11 \times 3 = 33$ L.Final milk = $26.2$ L, so final water = $33 - 26.2 = 6.8$ L.Removing 28 L of mixture does not change the milk-to-water ratio.After removal (before adding milk), total = $45 - 28 = 17$ L.Milk in this remaining mixture = final milk minus added milk = $26.2 - 16 = 10.2$ L.Water in this = $17 - 10.2 = 6.8$ L (matches final water since no water added).So initial milk : water ratio = $10.2 : 6.8 = 102 : 68 = 51 : 34 = 3 : 2$ (dividing by 17).Water fraction = $\frac{2}{3+2} = \frac{2}{5}$.Water percentage = $\frac{2}{5} \times 100 = 40\%$.Answer:40% (Option E)