in an exam every question correctly answerd fetches 2 marks. each question wrongly answerd loses one mark.  Ram and Shyam wrote this exam. Ram attempted A certain number of questions and 20% of them went wrong. Shyam attempted a certain number of questions and 10% of them went wrong. Ram got 33 marks more than the pass mark. Shyam got 48 marks more than the pass mark. the two of them together attempted a total of 100 questions. what is the pass mark of the examination? (a) 59 (b) 43 (c) 47 (d) 37 the total marks scored by ram and shyam is how much more or less than maximum marks of the examination? (a) 0 (b) 8 more (c) 12 less (d) cannot be determined

Let's solve the problem step by step.

### Let:
- \( x \) be the number of questions Ram attempted.
- \( y \) be the number of questions Shyam attempted.

### Given:
1. \( x + y = 100 \) (total number of questions attempted by both).
2. Ram got 33 marks more than the pass mark.
3. Shyam got 48 marks more than the pass mark.
4. 20% of Ram's attempted questions were wrong.
5. 10% of Shyam's attempted questions were wrong.

### Step 1: Calculate the number of correct and wrong answers.
- Ram:
  - Wrong answers: \( 0.2x \)
  - Correct answers: \( 0.8x \)
  - Ram's marks: \( 2(0.8x) - 1(0.2x) = 1.4x \)

- Shyam:
  - Wrong answers: \( 0.1y \)
  - Correct answers: \( 0.9y \)
  - Shyam's marks: \( 2(0.9y) - 1(0.1y) = 1.7y \)

### Step 2: Express the marks in terms of the pass mark.
- Ram's marks: \( 1.4x = P + 33 \)
- Shyam's marks: \( 1.7y = P + 48 \)

### Step 3: Set up the equations.
- \( 1.4x = P + 33 \)  ⟶ (1)
- \( 1.7y = P + 48 \)  ⟶ (2)
- \( x + y = 100 \) ⟶ (3)

### Step 4: Solve for \( x \), \( y \), and \( P \).

From equation (1):
\[ P = 1.4x - 33 \]

From equation (2):
\[ P = 1.7y - 48 \]

Equating the two expressions for \( P \):
\[ 1.4x - 33 = 1.7y - 48 \]

\[ 1.4x - 1.7y = -15 \]

\[ 14x - 17y = -150 \]  ⟶ (4)

Using equation (3):
\[ y = 100 - x \]

Substitute \( y = 100 - x \) into equation (4):
\[ 14x - 17(100 - x) = -150 \]

\[ 14x - 1700 + 17x = -150 \]

\[ 31x = 1550 \]

\[ x = 50 \]

So, \( y = 100 - x = 50 \).

### Step 5: Calculate the pass mark \( P \).

Substitute \( x = 50 \) into equation (1):
\[ 1.4(50) = P + 33 \]

\[ 70 = P + 33 \]

\[ P = 37 \]

Thus, the pass mark is \( \boxed{37} \).

### Step 6: Calculate the total marks scored by Ram and Shyam.
- Ram's marks: \( 1.4(50) = 70 \)
- Shyam's marks: \( 1.7(50) = 85 \)
- Total marks scored by both: \( 70 + 85 = 155 \)

### Step 7: Determine how much more or less this is compared to the maximum marks.
- Maximum marks for 100 questions (all correct): \( 2(100) = 200 \)
- Difference: \( 200 - 155 = 45 \) marks less.

So, the total marks scored by Ram and Shyam is \( \boxed{45 \text{ less}} \) than the maximum marks.

**Final Answers:**
- Pass mark: \( \boxed{37} \) (option d).
- The total marks scored by Ram and Shyam is \( \boxed{45 \text{ less}} \) than the maximum marks.

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Would you like any further details or have any questions? Here are some related problems you might find interesting:

1. If Ram attempted 60 questions instead, what would be the pass mark?
2. How would the pass mark change if Shyam had 20% wrong answers instead of 10%?
3. What is the difference in marks between Ram and Shyam if they both scored equally above the pass mark?
4. How many questions would Shyam have needed to answer to score 70 marks above the pass mark?
5. What would be the effect on the pass mark if there were a penalty of 2 marks for every wrong answer?

**Tip:** To tackle similar problems, focus on breaking down the problem into smaller parts and set up equations based on the information provided.

Learn how to solve a complex exam marks calculation problem involving Ram and Shyam. Understand the process of determining the pass mark based on their scores and the percentage of correct and wrong answers. Suitable for high school students.

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