Which student got the highest percentage in the class?
Show Hint
To quickly compare totals without adding every term fully, look at how the scores deviate from a baseline of 80:
- Sarika: $+7 - 2 - 3 + 7 + 0 = +9$
- Purvansh: $+2 + 1 + 4 + 3 + 0 = +10$
- Anjali: $+5 + 2 - 5 + 4 - 1 = +5$
Purvansh clearly has the highest positive deviation ($+10$), making him the top scorer.
Step 1: Understanding the Concept:
To find the student with the highest overall percentage, we need to calculate the sum of the marks obtained by each student across all five subjects.
Since the maximum marks for each subject are equal, the student with the highest total marks will also have the highest overall percentage. Step 2: Detailed Explanation:
Let us calculate the total marks for the four students listed in the options to find the highest score:
1. Sarika (Option A):
\[ \text{Total} = 87 (\text{Eng}) + 78 (\text{Math}) + 77 (\text{Phys}) + 87 (\text{Chem}) + 80 (\text{Hindi}) \]
\[ \text{Total} = 165 + 77 + 87 + 80 = 242 + 87 + 80 = 329 + 80 = 409 \]
2. Purvansh (Option B):
\[ \text{Total} = 82 (\text{Eng}) + 81 (\text{Math}) + 84 (\text{Phys}) + 83 (\text{Chem}) + 80 (\text{Hindi}) \]
\[ \text{Total} = 163 + 84 + 83 + 80 = 247 + 83 + 80 = 330 + 80 = 410 \]
3. Parth (Option C):
\[ \text{Total} = 70 (\text{Eng}) + 74 (\text{Math}) + 72 (\text{Phys}) + 75 (\text{Chem}) + 72 (\text{Hindi}) \]
\[ \text{Total} = 144 + 72 + 75 + 72 = 216 + 75 + 72 = 291 + 72 = 363 \]
4. Anjali (Option D):
\[ \text{Total} = 85 (\text{Eng}) + 82 (\text{Math}) + 75 (\text{Phys}) + 84 (\text{Chem}) + 79 (\text{Hindi}) \]
\[ \text{Total} = 167 + 75 + 84 + 79 = 242 + 84 + 79 = 326 + 79 = 405 \]
Let us compare the total marks of these students:
- Sarika: 409
- Purvansh: 410
- Parth: 363
- Anjali: 405
Purvansh has the highest total marks of 410.
His overall percentage is:
\[ \text{Percentage} = \frac{410}{500} \times 100 = 82% \]
Therefore, Purvansh secured the highest percentage in the class. Step 3: Final Answer:
The correct option is (B).
