Examination Score Calculation with Weights

This problem involves calculating a missing score in an examination where different papers have different weightages. We need to determine Jonathan's score in Paper B given his score in Paper A, the maximum marks for each paper, the weights of the papers, and his overall examination percentage.

Given Information

• Maximum mark for Paper A = 10
• Maximum mark for Paper B = 10
• Weight ratio of Paper A to Paper B = 2:1
• Jonathan's score in Paper A = 8 out of 10
• Jonathan's overall percentage in the examination = 70%

Understanding Weighted Marks

In this examination, the scores from Paper A and Paper B do not contribute equally to the overall percentage. Paper A has a weightage twice that of Paper B. Let's denote the weights as $w_A$ and $w_B$. According to the given ratio, we can set:

• $w_A = 2$
• $w_B = 1$

The maximum marks for both papers are $M_A = 10$ and $M_B = 10$. Jonathan's score in Paper A is $S_A = 8$. Let his score in Paper B be $S_B$.

Calculating Total Maximum Weighted Marks

The total maximum possible marks for the examination, considering the weights, are calculated as follows:

Total Maximum Weighted Marks = $(w_A \times M_A) + (w_B \times M_B)$

Substituting the values:

Total Maximum Weighted Marks = $(2 \times 10) + (1 \times 10) = 20 + 10 = 30$.

Calculating Total Weighted Score Obtained

Jonathan achieved an overall score of 70% in the examination. This percentage is calculated based on the total maximum weighted marks.

Total Weighted Score Obtained = 70% of Total Maximum Weighted Marks

Total Weighted Score Obtained = $\frac{70}{100} \times 30 = 0.70 \times 30 = 21$.

Calculating Weighted Score for Paper A

Jonathan's score in Paper A (8 out of 10) contributes to the total score based on its weight ($w_A = 2$).

Weighted Score for Paper A = $w_A \times S_A$

Weighted Score for Paper A = $2 \times 8 = 16$.

Calculating Weighted Score for Paper B

The total weighted score obtained (21) is the sum of the weighted scores from Paper A and Paper B.

Total Weighted Score Obtained = Weighted Score for Paper A + Weighted Score for Paper B

So, Weighted Score for Paper B = Total Weighted Score Obtained - Weighted Score for Paper A

Weighted Score for Paper B = $21 - 16 = 5$.

Finding the Score in Paper B

The weighted score for Paper B (which is 5) is calculated using its weight ($w_B = 1$) and Jonathan's actual score ($S_B$).

Weighted Score for Paper B = $w_B \times S_B$

$5 = 1 \times S_B$

$S_B = \frac{5}{1} = 5$.

Therefore, Jonathan scored 5 in Paper B.

Conclusion

Jonathan scored 5 out of 10 in Paper B.