IBPS PO Mains 12 Oct 2025 Shift 1 Paper

Concept:A statement is sufficient only if it leads to a unique value of $X$. Use the simple interest and compound interest formulas to check each statement.Explanation:Given: Principal $P = \text{Rs. }2,000$, rate $X\%$ per annum, time $T$ years, and $X$ is an integer multiple of $T$.Simple interest formula: $SI = \frac{P \times X \times T}{100}$.From Statement I: $SI = 2160$.So, $2160 = \frac{2000 \times X \times T}{100}$, which gives $2160 = 20XT$.Therefore, $XT = 108$.Since $X$ is a multiple of $T$, let $X = kT$, where $k$ is an integer.Then $kT^2 = 108$. Multiple pairs satisfy this, such as $(X,T) = (108,1), (54,2), (36,3), (18,6)$.Thus, Statement I alone is not sufficient.From Statement II: Compound interest at $20\%$ per annum for $0.5T$ years is Rs. 1,456.Amount after $0.5T$ years: $2000 + 1456 = 3456$.Using $A = P\left(1+\frac{R}{100}\right)^n$: $3456 = 2000(1.2)^{0.5T}$.So, $(1.2)^{0.5T} = 1.728 = (1.2)^3$.Hence, $0.5T = 3$, giving $T = 6$ years.This statement gives only $T$, not $X$, so it is also insufficient alone.Combining both statements: From Statement II, $T = 6$.Substitute into Statement I: $X \times 6 = 108$.Therefore, $X = 18\%$.Both statements together are necessary and sufficient.Answer:Both Statements I and II together are required.Correct option: D. Both Statements I and II together.