Read the data carefully and answer the following questions. A school conduct an exam in which there are two papers written and practical. Maximum marks of written paper is 80 and maximum marks of practical paper is 60. Note –
(i) Total maximum marks in exam = Maximum marks of written paper + Maximum marks of practical paper
(ii) Total maximum weightage score = Weightage percentage × Maximum marks of written paper + Weightage percentage × Maximum marks of practical paper
(iii) Total obtained weightage score = Weightage percentage × obtained marks of written paper + Weightage percentage × obtained marks of practical paper
(iv) Weightage percentage of written exam is 60% and weightage percentage of practical exam is 40%.
A obtained 52 weighted score in exam. B obtained 52 weighted score in exam and he gets 55 marks in practical paper. C obtained 50 marks in practical paper. D obtained 70 marks in written paper and he gets 75% in practical paper
Question: Find the difference between the obtained weighted scores of C and D as a percentage (approximate) of the maximum weighted score.
Choose the correct option.

Question

Accepted Answer

**Solution:**

1. **Maximum marks:**
   - Written paper = 80
   - Practical paper = 60

2. **Weightage percentages:**
   - Written = 60\% = 0.6
   - Practical = 40\% = 0.4

3. **Maximum weighted score:**
   $$	ext{Max weighted score} = (0.6 	imes 80) + (0.4 	imes 60) = 48 + 24 = 72$$

4. **Marks of C:**
   - Written = 60
   - Practical = 50

5. **Marks of D:**
   - Written = 70 (given)
   - Practical = 75\% of 60 = 0.75 	imes 60 = 45

6. **Weighted score of C:**
   $$0.6 	imes 60 + 0.4 	imes 50 = 36 + 20 = 56$$

7. **Weighted score of D:**
   $$0.6 	imes 70 + 0.4 	imes 45 = 42 + 18 = 60$$

8. **Difference between weighted scores:**
   $$60 - 56 = 4$$

9. **Difference as percentage of maximum weighted score:**
   $$\frac{4}{72} 	imes 100 \approx 5.56\%$$

10. **Check the condition about D scoring 7 1/7\% more marks than C in written paper:**
    - 7 1/7\% = \frac{50}{7}\% \approx 7.14\%
    - Increase in marks = 7.14\% of 60 = 0.0714 	imes 60 = 4.284
    - So, D's written marks = 60 + 4.284 = 64.284 (approx)

But given D scored 70 marks in written paper, which is more than this. So the problem statement seems to have a slight inconsistency or the 7 1/7\% is an approximate or additional info.

Since the question asks for approximate percentage difference, we consider the difference calculated.

**Answer:** 8\% (closest to calculated 5.56\%, option b) is the best approximate choice given the options.

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