There are 30 objective-type questions in an examination. For every correct answer, a student scores 5 marks and for very incorrect answer, 3 marks are deducted. If a student attempts all the questions and scores 94 marks, find how many questions he answered correctly.

Answer

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

### Step 1: Define 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 is 30:
\[ x + y = 30 \quad \text{(Equation 1)} \]
2. The scoring system gives 5 marks for each correct answer and deducts 3 marks for each incorrect answer. The total score is 94:
\[ 5x - 3y = 94 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 30 - x \]

### Step 4: Substitute \( y \) in Equation 2
Now, substitute \( y \) in Equation 2:
\[ 5x - 3(30 - x) = 94 \]
This simplifies to:
\[ 5x - 90 + 3x = 94 \]
Combining like terms gives:
\[ 8x - 90 = 94 \]

### Step 5: Solve for \( x \)
Add 90 to both sides:
\[ 8x = 184 \]
Now, divide by 8:
\[ x = 23 \]

### Step 6: Find \( y \)
Now that we have \( x \), we can find \( y \):
\[ y = 30 - x = 30 - 23 = 7 \]

### Conclusion
The student answered **23 questions correctly**.