Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given 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; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the average monthly income per family member? I. Each male earns ₹ 1250 a month and each female earns ₹ 1050 a month. II. Ratio of males to females in the family is 2 : 1.

### Concept & Logic To determine the average income per member of a family comprising only males and females, we need the individual incomes of males and females, along with the numerical ratio of males to females to compute a weighted average. $$ \text{Average} = \frac{(\text{Male Income} \times \text{Number of Males}) + (\text{Female Income} \times \text{Number of Females})}{\text{Total Members}} $$ ### Step-by-Step Solution * **From Statement I:** We are given the incomes. Male income = ₹ 1250, Female income = ₹ 1050. However, without knowing how many males and females there are (or their ratio), we cannot calculate the family average. Statement I alone is not sufficient. * **From Statement II:** We are given the ratio of males to females as $2:1$. Without knowing their respective incomes, we cannot calculate the average income. Statement II alone is not sufficient. * **Combining Statements I and II:** Let the number of males be $2x$ and females be $1x$. $$ \text{Total Income} = (1250 \times 2x) + (1050 \times 1x) = 2500x + 1050x = 3550x $$ $$ \text{Total Members} = 2x + 1x = 3x $$ $$ \text{Average Income} = \frac{3550x}{3x} = \frac{3550}{3} $$ Since the $x$ cancels out, we can find a definitive numerical average. Both statements are required. ### Exam Strategy & Shortcut Recognize the elements of a weighted average equation. Statement I provides the "values" and Statement II provides the "weights" (ratios). Since you have both pieces of the puzzle when combining them, and no missing variables, you can immediately conclude (e) without doing the math. ### Common Pitfall Students often think that the exact number of family members (e.g., 4 males, 2 females) is required. They might choose "not sufficient" because only a ratio is given. Remember that in weighted averages, ratios are perfectly sufficient because the multiplier variables cancel out in the fraction. ### Final Answer **Therefore, the correct answer is Data in both Statements I and II together are necessary.**