judge students’ grasp over concepts discussed in this week. To discourage students from making wild guesses, she awarded +4 for correct responses and -1 for incorrect responses. No marks were awarded or deducted for unattempted questions. The top scorer of the last weekly test was Afzal. Afzal scored 300 marks. If he attempted all the 200 questions, then can you tell us how many questions were answered correctly by him.
Anjali started conducting weekly tests on Friday evening. The marks in this test were used as a metric to judge students’ grasp over concepts discussed in this week. To discourage students from making wild guesses, she awarded +4 for correct responses and -1 for incorrect responses. No marks were awarded or deducted for unattempted questions. The top scorer of the last weekly test was Afzal. Afzal scored 300 marks. If he attempted all the 200 questions, then can you tell us how many questions were answered correctly by him.
The Correct Answer and Explanation is:
Answer: Afzal answered 85 questions correctly.
Explanation:
We are given:
- Afzal attempted all 200 questions.
- He received:
- +4 marks for each correct answer.
- –1 mark for each incorrect answer.
- 0 marks for unattempted questions (but Afzal attempted all).
- Total score = 300 marks.
Let:
- xx = number of correct answers
- Then, 200−x200 – x = number of incorrect answers (since he attempted all)
Step 1: Form the equation
Each correct answer gives 4 marks → 4x4x
Each incorrect answer loses 1 mark → −1(200−x)-1(200 – x)
So, total score = 4x−1(200−x)=3004x – 1(200 – x) = 300
Step 2: Solve the equation
4x−(200−x)=300⇒4x−200+x=300⇒5x−200=300⇒5x=500⇒x=1004x – (200 – x) = 300 \Rightarrow 4x – 200 + x = 300 \Rightarrow 5x – 200 = 300 \Rightarrow 5x = 500 \Rightarrow x = 100
Wait! That gives x = 100, but we said Afzal scored 300. Let’s double-check this.
Actually, there is an error in the final step above. Let’s rework the equation carefully.
4x−1(200−x)=300⇒4x−200+x=300⇒5x−200=300⇒5x=500⇒x=1004x – 1(200 – x) = 300 \Rightarrow 4x – 200 + x = 300 \Rightarrow 5x – 200 = 300 \Rightarrow 5x = 500 \Rightarrow x = 100
Ah! It seems the previous steps are indeed correct. So Afzal answered 100 questions correctly, not 85.
Let’s recalculate his total score with this result:
- Correct answers = 100 → 100×4=400100 \times 4 = 400
- Incorrect answers = 200−100=100200 – 100 = 100 → 100×−1=−100100 \times -1 = -100
- Total score = 400−100=300400 – 100 = 300
✅ This matches the score given in the problem.
Conclusion:
Afzal answered 100 questions correctly, and the remaining 100 were incorrect. His total score of 300 matches the marking scheme: 100×4−100×1=400−100=300100 \times 4 – 100 \times 1 = 400 – 100 = 300
So, the correct answer is 100 correct answers.
