A student gets 4 marks for a correct answer and 1 mark is deducted for a wrong answer. If she has done 80 questions at all and she has gotten only 240 marks. The correct answers she has attempted is :

Options

A. 40
B. 60
C. 64
D. can't be determined

Answer

To solve the problem step by step, we will set up equations based on the information given and solve for the number of correct answers attempted by the student.

### Step 1: Define the Variables
Let:
- \( x \) = number of correct answers
- \( y \) = number of incorrect answers

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of questions attempted is 80:
\[ x + y = 80 \quad \text{(Equation 1)} \]
2. The total marks obtained is 240, where the student earns 4 marks for each correct answer and loses 1 mark for each incorrect answer:
\[ 4x - y = 240 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We have two equations:
1. \( x + y = 80 \)
2. \( 4x - y = 240 \)

We can solve these equations simultaneously. First, we can express \( y \) from Equation 1:
\[ y = 80 - x \]

### Step 4: Substitute \( y \) in Equation 2
Now, substitute \( y \) in Equation 2:
\[ 4x - (80 - x) = 240 \]
Simplifying this gives:
\[ 4x - 80 + x = 240 \]
\[ 5x - 80 = 240 \]

### Step 5: Isolate \( x \)
Now, add 80 to both sides:
\[ 5x = 240 + 80 \]
\[ 5x = 320 \]
Now, divide both sides by 5:
\[ x = \frac{320}{5} \]
\[ x = 64 \]

### Conclusion
The number of correct answers the student has attempted is \( \boxed{64} \).

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