Directions: Each of the questions below consists of a statement and/or a question and two statements labelled I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; and Give answer (e) if the data in both Statements I and II are necessary to answer the question. Vipin's and Javed's salaries are in the proportion of $4 : 3$ respectively. What is Vipin's salary? I. Javed's salary is $75\%$ that of Vipin's salary. II. Javed's salary is ₹ $4500$.

### Concept & Redundant Information When a prompt establishes a ratio between two variables, you need an exact numerical value for one of the variables (or their sum/difference) to find the absolute value of the other. Restating the ratio provides no new mathematical power. ### Step-by-Step Solution * **Analyzing the Prompt:** * Let Vipin's salary be $V$ and Javed's salary be $J$. * Given: $V : J = 4 : 3$. This means $V = \frac{4}{3}J$ and $J = \frac{3}{4}V$. * **Analyzing Statement I:** * Given: Javed's salary is $75\%$ of Vipin's salary. * Mathematically, this is $J = 0.75V$, which simplifies to $J = \frac{3}{4}V$. * This is the exact same information already provided in the main question prompt. It does not give us a concrete number to calculate Vipin's absolute salary. * Therefore, Statement I is not sufficient. * **Analyzing Statement II:** * Given: Javed's salary ($J$) = ₹ $4500$. * Using the ratio from the prompt: $V / 4500 = 4 / 3$. * Solving for $V$: $V = (4 / 3) \times 4500 = 6000$. * Because we can calculate an exact numerical value for Vipin's salary, Statement II alone is sufficient. ### Exam Strategy & Shortcut Watch out for statements that simply paraphrase the main question prompt using different phrasing (like converting a ratio to a percentage). Recognize that $4:3$ means the smaller number is $3/4$ (or $75\%$) of the larger number. Once you spot this, you can instantly eliminate Statement I without doing any math. ### Common Pitfall A common mistake is reading Statement I too fast and confusing which salary is a percentage of which, or failing to realize it is merely restating the premise. ### Final Answer Therefore, the correct answer is **if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question**.