The following table gives the marks obtained by a student in the first and second semester examinations in four subjects in a given year. | Subjects | 1st Semester | 2nd Semester | Maximum Marks | | :--- | :---: | :---: | :---: | | Physics | 35 | 30 | 50 | | Chemistry | 30 | 25 | 50 | | Mathematics | 65 | 45 | 100 | | Social Science | 80 | 85 | 100 | The aggregate percentage of marks obtained by the student in the given year is nearly

### Concept & Strategy To find the aggregate percentage for the entire year, we must calculate the total marks obtained across both semesters and divide it by the total maximum marks available for both semesters combined. $$ \text{Aggregate Percentage} = \left( \frac{\text{Total Marks Obtained in Year}}{\text{Total Maximum Marks for Year}} \right) \times 100 $$ ### Step-by-Step Solution * **Deduction (Maximum Marks):** * The "Maximum Marks" column denotes the total marks per subject per semester. * Maximum marks for one semester $= 50 + 50 + 100 + 100 = 300$. * Since there are two semesters in the year, the grand total maximum marks $= 300 \times 2 = 600$. * **Calculation (Marks Obtained):** * Total marks obtained in 1st Semester $= 35 + 30 + 65 + 80 = 210$. * Total marks obtained in 2nd Semester $= 30 + 25 + 45 + 85 = 185$. * Total marks obtained in the year $= 210 + 185 = 395$. * **Final Percentage Calculation:** * $\text{Percentage} = \left( \frac{395}{600} \right) \times 100$ * $\text{Percentage} = \frac{395}{6}$ * $395 \div 6 = 65.833...$ * Rounding to the nearest whole number gives $66$. ### Exam Strategy & Shortcut Instead of adding columns vertically, you can add horizontally to find the total per subject first, which sometimes creates easier numbers: Physics: $35 + 30 = 65$ out of $100$ Chemistry: $30 + 25 = 55$ out of $100$ Maths: $65 + 45 = 110$ out of $200$ Social: $80 + 85 = 165$ out of $200$ Total Obtained $= 65 + 55 + 110 + 165 = 120 + 275 = 395$. Total Max $= 100 + 100 + 200 + 200 = 600$. $\frac{395}{6}$ is just under $\frac{400}{6}$. Since $\frac{400}{6} = 66.66$, $\frac{395}{6}$ will be very close to $66$. ### Common Pitfall The most common trap is misinterpreting the "Maximum Marks" column. Many students assume the maximum marks listed ($300$ total) are for the whole year, rather than per semester. If you divide $395$ by $300$, you would get an impossible percentage over $100\%$, which should immediately alert you to double the denominator. ### Final Answer **Therefore, the correct answer is 66.**