In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 200 questions and scored in all 200 marks. The number of questions he answered correctly was

### Concept & Strategy This is a classic penalty scoring problem. It is best solved using the "Deviation Method" (or assumed total method), which calculates the total possible score if all questions were correct, and then divides the "loss" in marks by the penalty per wrong answer to find the number of incorrect answers. $$ \text{Wrong Answers} = \frac{\text{Maximum Possible Score} - \text{Actual Score}}{\text{Marks per Correct Answer} + \text{Penalty per Wrong Answer}} $$ ### Step-by-Step Solution * **Assume all are correct:** If the student answered all 200 questions correctly, the maximum possible score would be $200 \times 4 = 800$ marks. * **Calculate the total loss:** The student actually scored 200 marks. The marks lost due to wrong answers = $800 - 200 = 600$ marks. * **Determine loss per wrong answer:** Every wrong answer costs the student 4 marks (the marks they *would* have gotten) PLUS 1 mark (the negative penalty). Total loss per wrong answer = $4 + 1 = 5$ marks. * **Find number of wrong answers:** Total wrong answers = $\frac{600}{5} = 120$. * **Find number of correct answers:** Total questions minus wrong answers = $200 - 120 = 80$. ### Exam Strategy & Shortcut Using the algebraic method ($4c - 1(200 - c) = 200$) works, but the assumed total method is much faster mentally. You can simply think: "Max score is 800. He lost 600. Each mistake costs 5 points. $600 / 5 = 120$ wrong. So $80$ right." This eliminates algebra entirely. ### Common Pitfall The most common mistake is assuming the loss per wrong answer is just the penalty mark ($1$). This leads to calculating the wrong answers as $600 / 1 = 600$, which makes no sense. You must remember that getting a question wrong also means forfeiting the positive marks it carried. ### Final Answer **Therefore, the correct answer is 80.**