Abhinav scores 80% in Physics and 66% in Chemistry, each subject having a maximum of 100 marks. Mathematics has a maximum of 200 marks. If Abhinav scores an overall 80% across all three subjects together, what percentage does he score in Mathematics?

Introduction / Context:
This question checks your ability to handle percentages when different subjects carry different maximum marks. Instead of treating each subject equally, you must work with total marks and find the unknown score in Mathematics so that the overall percentage condition is satisfied. This type of problem is common in examination and report card style aptitude questions.

Given Data / Assumptions:

Maximum marks in Physics = 100.

Maximum marks in Chemistry = 100.

Maximum marks in Mathematics = 200.

Abhinav scores 80% in Physics.

Abhinav scores 66% in Chemistry.

Overall percentage across all three subjects is 80% of total marks.

Concept / Approach:
First, convert each percentage to actual marks using the formula:
obtained marks = (percentage / 100) * maximum marks.
Then add all obtained marks to get Abhinav total marks. Since the total maximum marks across all three subjects are known, we can use the condition that his overall percentage is 80% to find the required marks in Mathematics. Finally, convert those Mathematics marks back into a percentage out of 200.

Step-by-Step Solution:
Step 1: Maximum total marks = 100 (Physics) + 100 (Chemistry) + 200 (Mathematics) = 400.Step 2: Marks in Physics = 80% of 100 = 0.80 * 100 = 80.Step 3: Marks in Chemistry = 66% of 100 = 0.66 * 100 = 66.Step 4: Let marks in Mathematics be M.Step 5: Overall percentage is 80%, so total marks obtained = 80% of 400 = 0.80 * 400 = 320.Step 6: Therefore 80 + 66 + M = 320.Step 7: So M = 320 – (80 + 66) = 320 – 146 = 174.Step 8: Percentage in Mathematics = (174 / 200) * 100 = 87%.

Verification / Alternative check:
Check the computed values: Physics 80 marks, Chemistry 66 marks, Mathematics 174 marks. Total = 320 out of 400. 320 / 400 * 100 = 80%, which matches the required overall percentage. Therefore 87% in Mathematics is fully consistent.

Why Other Options Are Wrong:
74% and 83% both give total marks less than 320 and so the overall percentage would be lower than 80%.
84% gives Mathematics marks 168, making the total 314, which corresponds to 78.5% overall, not 80%.
80% in Mathematics would give 160 marks and total 306, again below the required total marks.

Common Pitfalls:
Many students simply average the percentages of three subjects without weighting them according to maximum marks. This leads to incorrect results because Mathematics is worth twice as many marks as each of the other subjects. Always base your calculations on actual marks and total maximum marks when different papers have different weightage.

Final Answer:
Abhinav score in Mathematics is 87%.