Direction: Each of the questions below consists of a question-statement and two statements I and II are given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Give answer. What will be the total marks of Subodh in physics? I. The average marks of Subodh in History, Geography and Chemistry are $75$. II. His average marks in History, Geography and Physics are $78$.

### Concept & Logic To find the exact value of a single variable (marks in Physics), we need an equation where Physics is the only unknown, or a system of equations that allows us to isolate it. We apply the basic average formula: $$Sum = Average \times Number of Subjects$$ ### Step-by-Step Solution **Evaluating Statement I alone:** * Given: Average of History (H), Geography (G), and Chemistry (C) = $75$. * Equation: H + G + C = $3 \times 75 = 225$. * This statement contains no information about Physics (P). It is insufficient. **Evaluating Statement II alone:** * Given: Average of History (H), Geography (G), and Physics (P) = $78$. * Equation: H + G + P = $3 \times 78 = 234$. * We have one equation with three variables. We cannot determine P without knowing the combined sum of H and G. It is insufficient. **Evaluating Statements I and II combined:** * From I: H + G + C = $225$ * From II: H + G + P = $234$ * Subtracting the first equation from the second gives: P - C = $9$. * This tells us Physics marks are $9$ more than Chemistry marks. However, without knowing the absolute marks in Chemistry, we still cannot determine the exact marks in Physics. ### Exam Strategy & Shortcut Look at the variables involved. We want to find P. Statement I gives variables (H, G, C). No P. Insufficient. Statement II gives variables (H, G, P). Three unknowns, one equation. Insufficient. Combining them gives (H, G, C) and (H, G, P). We have 4 unknowns (H, G, C, P) but only 2 independent equations. Mathematically, it is impossible to solve for a unique value of P. You can instantly conclude that both statements together are insufficient without multiplying $75$ by $3$ or $78$ by $3$. ### Common Pitfall Students often see two equations with overlapping variables (History and Geography) and automatically assume combining them will solve the problem. Always check if you are left with more unknowns than equations. Here, subtracting leaves P and C, which still cannot be solved. ### Final Answer **Therefore, the correct answer is The data in both Statement I and II are not sufficient to answer the question.**