In an examination , one mark is awarded for every correct answer , while `(1)/(4)` mark is deducted for every worng answer . If a students gets 90 marks by answering 120 questions , then how many question did she answer correctly ?

Options

A. 96
B. 100
C. 90
D. 95

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information provided.

### Step 1: Define Variables
Let:
- \( x \) = number of questions answered correctly
- \( y \) = number of questions answered incorrectly

### Step 2: Set Up the Equations
From the problem statement, we know:
1. The total number of questions answered is 120:
\[ x + y = 120 \]
2. The scoring system awards 1 mark for each correct answer and deducts \( \frac{1}{4} \) mark for each incorrect answer. The total score is 90:
\[ x - \frac{1}{4}y = 90 \]

### Step 3: Solve the First Equation for \( y \)
From the first equation \( x + y = 120 \), we can express \( y \) in terms of \( x \):
\[ y = 120 - x \]

### Step 4: Substitute \( y \) in the Second Equation
Now, substitute \( y \) in the second equation:
\[ x - \frac{1}{4}(120 - x) = 90 \]

### Step 5: Simplify the Equation
Distributing \( \frac{1}{4} \):
\[ x - 30 + \frac{1}{4}x = 90 \]
Combine like terms:
\[ \frac{5}{4}x - 30 = 90 \]

### Step 6: Isolate \( x \)
Add 30 to both sides:
\[ \frac{5}{4}x = 120 \]
Multiply both sides by \( \frac{4}{5} \):
\[ x = 120 \times \frac{4}{5} = 96 \]

### Step 7: Conclusion
The number of questions answered correctly is:
\[ \boxed{96} \]