The marks obtained by a student are given below. What is his total percentage in all the subjects? | Subjects | Total Marks | Marks Obtained | | :--- | :---: | :---: | | Mathematics | 100 | 100 | | Science | 100 | 84 | | Social Studies | 100 | 67 | | English | 50 | 25 | | Hindi | 50 | 24 |

### Concept & Formula To find the aggregate or total percentage across multiple subjects, you must sum up all the maximum possible marks to find the overall denominator, and sum up all the obtained marks to find the overall numerator. $$ \text{Total Percentage} = \left( \frac{\text{Sum of Marks Obtained}}{\text{Sum of Total Marks}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Maximum marks per subject: $100, 100, 100, 50, 50$ * Marks obtained per subject: $100, 84, 67, 25, 24$ * **Calculation:** * Calculate the grand total of maximum marks: * $100 + 100 + 100 + 50 + 50 = 400$ * Calculate the grand total of marks obtained: * $100 + 84 + 67 + 25 + 24 = 300$ * Apply the percentage formula: * $\text{Percentage} = \left( \frac{300}{400} \right) \times 100$ * $\text{Percentage} = \frac{3}{4} \times 100 = 75\%$ ### Exam Strategy & Shortcut Addition speed is the key here. Group numbers that complement each other: For obtained marks: $(25 + 24) = 49$. Then $(84 + 67) = 151$. Finally, $151 + 49 + 100 = 300$. Recognizing that $\frac{300}{400}$ reduces to the standard fraction $\frac{3}{4}$ instantly gives you $75\%$ without multiplying by $100$. ### Common Pitfall A common mistake is calculating the percentage for each subject individually and then averaging those percentages. Because the "Total Marks" (denominators) are not uniform ($100$ vs $50$), taking a simple average of individual percentages will yield a mathematically incorrect result. Always aggregate the raw scores first. ### Final Answer **Therefore, the correct answer is 75%.**