IBPS PO Mains 30 Nov 2024 Shift 2 Paper

Concept:To determine a unique ratio of three ages, we need consistent independent equations relating $a$, $b$, and $c$.Statement III creates ambiguity through absolute differences, and no valid unique set of ages is obtained.Explanation:Let the present ages of A, B, and C be $a$, $b$, and $c$.From Statement I: $\frac{a+5}{b+5} = \frac{4}{5} \Rightarrow 5a - 4b = -5$.From Statement II: $\frac{a-7}{c-7} = \frac{3}{4} \Rightarrow 4a - 3c = 7$.From Statement III: $|a-b| = 5$ and $|b-c| = 5$.Combining I with $|a-b| = 5$, the only valid positive case is $b = a+5$.So, $5a - 4(a+5) = -5 \Rightarrow a = 15$, $b = 20$.Using II: $4(15) - 3c = 7 \Rightarrow c = \frac{53}{3}$.But $|b - c| = \left|20 - \frac{53}{3}\right| = \frac{7}{3} \neq 5$.Thus, all three statements contradict each other.Also, Statements II and III together allow multiple possible age sets.Therefore, the ratio of ages after 10 years cannot be uniquely determined.Answer:D. All three statements together are not sufficient.