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. What is the present age of the mother? (M.A.T., 2007) I. Father's age is 8 years more than the mother's age. Father got married at the age of 28 years. II. Present age of the father is 30 years. Four years back the ratio of mother's age to father's age was $12 : 13$.

### Concept & Age Ratios To find a specific person's age, we need an exact value anchored to a point in time (present, past, or future) and a relative relationship to that value. ### Step-by-Step Solution * **Analyzing Statement I:** * We are given: Father's Age = Mother's Age + 8. * We are given: Father married at 28. * This provides a relative relationship between their ages but no anchor to the *present* age. We do not know how many years ago the father got married. * Therefore, Statement I is not sufficient. * **Analyzing Statement II:** * We are given: Present age of Father = 30 years. * We are given: 4 years ago, (Mother's Age - 4) / (Father's Age - 4) = 12 / 13. * Father's age 4 years ago = 30 - 4 = 26. * Substitute this into the ratio: (Mother's Age - 4) / 26 = 12 / 13. * Solving for Mother's age: Mother's Age - 4 = 26 * (12 / 13) = 24. * Mother's Age = 28 years. * Statement II provides both an absolute value and a definitive relationship, allowing us to find the exact present age of the mother. * Therefore, Statement II alone is sufficient. ### Exam Strategy & Shortcut When evaluating statements for age problems, instantly scan for a definitive anchor (a known number representing a current, past, or future age). Statement I lacks a present-day anchor, making it immediately insufficient. Statement II has an anchor (30 years) and a clear mathematical bridge to the target variable. ### Common Pitfall A common pitfall is attempting to combine the statements prematurely. Always evaluate Statement II completely independently before deciding if combination is necessary. ### 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**.