Directions: 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 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 was Altaf's income in 2010? I. His income for 2008, 2009 and 2010 was ₹ 3,00,000. II. He earned 20% more in 2009 than what he did in 2008.

Concept & Logic To solve for a specific variable in an equation with multiple unknowns, we need an equal number of distinct equations relating those variables. Step-by-Step Solution Given: We need to find the exact numerical value of Altaf's income in $2010$. Let incomes in $2008$, $2009$, and $2010$ be $x$, $y$, and $z$ respectively. We need to find $z$. Calculation / Deduction: * Analyzing Statement I: The combined income for three years is $3,00,000$. This gives the equation: $x + y + z = 3,00,000$. We have three unknowns and only one equation. Statement I is insufficient. * Analyzing Statement II: Income in $2009$ is $20\%$ more than in $2008$. This gives the equation: $y = 1.2x$. This tells us nothing about $2010$ ($z$). Statement II is insufficient. * Combining Both Statements: Substitute the second equation into the first: $x + 1.2x + z = 3,00,000$ $2.2x + z = 3,00,000$ * We are left with one linear equation containing two unknown variables ($x$ and $z$). It is mathematically impossible to isolate $z$ without additional information linking $z$ to either $x$ or $y$. Exam Strategy & Shortcut Variable Counting Method: Quickly list the unknowns: 2008, 2009, 2010 (3 variables). Statement I gives 1 equation (Sum). Statement II gives 1 equation (Ratio of 08 to 09). We have 2 equations total for 3 variables. The system is fundamentally unsolvable. Immediately select "not sufficient". Common Pitfall Assuming that an average or equal distribution applies when a total is given. Some students might incorrectly assume the $3,00,000$ is evenly split, or misread Statement II as applying an ongoing compounding $20\%$ increase year-over-year into 2010. Never assume trends that aren't explicitly stated. Final Answer **Therefore, the correct answer is If the data even in both statements I and II together are not sufficient.**