In an examination, a candidate attempts 90% of the total questions. Out of these 70% of his answers are correct. Each question carries 3 marks for the correct answer and (-1) mark for the wrong answer. If the marks secured by the candidate is 243, what is the total number of questions ?

Options

A. 110
B. 140
C. 150
D. 200

Answer

To solve the problem step by step, we will follow the information given in the question and derive the total number of questions.

### Step 1: Define the total number of questions
Let the total number of questions be \( x \).

### Step 2: Calculate the number of attempted questions
The candidate attempts 90% of the total questions. Therefore, the number of attempted questions is:
\[ \text{Attempted questions} = 0.9x \]

### Step 3: Calculate the number of correct answers
Out of the attempted questions, 70% of the answers are correct. Thus, the number of correct answers is:
\[ \text{Correct answers} = 0.7 \times (0.9x) = 0.63x \]

### Step 4: Calculate the number of incorrect answers
The remaining answers are incorrect. Since 70% are correct, 30% will be incorrect. Therefore, the number of incorrect answers is:
\[ \text{Incorrect answers} = 0.3 \times (0.9x) = 0.27x \]

### Step 5: Calculate the total marks secured
Each correct answer earns 3 marks, and each incorrect answer deducts 1 mark. The total marks secured by the candidate can be expressed as:
\[ \text{Total marks} = (3 \times \text{Correct answers}) + (-1 \times \text{Incorrect answers}) \]
Substituting the values we calculated:
\[ \text{Total marks} = (3 \times 0.63x) + (-1 \times 0.27x) \]
\[ \text{Total marks} = 1.89x - 0.27x = 1.62x \]

### Step 6: Set the equation for total marks
According to the problem, the total marks secured by the candidate is 243. Therefore, we set up the equation:
\[ 1.62x = 243 \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides by 1.62:
\[ x = \frac{243}{1.62} \]
Calculating the right side:
\[ x = 150 \]

### Conclusion
The total number of questions is \( \boxed{150} \).

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