Let's denote the total marks in the exam as $T$.

Step 1: Calculate the Passing Marks

The passing marks are given as 37.5% of the total marks: $\text{Passing Marks} = 0.375T$

Step 2: Calculate A's Marks

A scored 33.33% more than the passing marks. We can express this mathematically: $\text{A's Marks} = \text{Passing Marks} + 0.3333 \times \text{Passing Marks} = 1.3333 \times \text{Passing Marks}$ Substituting the expression for passing marks: $\text{A's Marks} = 1.3333 \times 0.375T = 0.5T$

Step 3: Calculate B's Marks

B failed by 50 marks. Thus, we can write: $\text{B's Marks} = \text{Passing Marks} - 50 = 0.375T - 50$

Step 4: Relationship Between A's and B's Marks

It is given that B's marks are 62.5% of A's marks: $\text{B's Marks} = 0.625 \times \text{A's Marks}$ Substituting the expressions for A's and B's marks: $0.375T - 50 = 0.625 \times 0.5T$ Simplifying the right side: $0.375T - 50 = 0.3125T$

Step 5: Solve for T

Rearranging the equation gives: $0.375T - 0.3125T = 50$ $0.0625T = 50$ $T = \frac{50}{0.0625} = 800$

Step 6: Find the Passing Marks

Now we can find the passing marks: $\text{Passing Marks} = 0.375 \times 800 = 300$

Conclusion

The passing marks are 300.

If you have any questions or need further details, feel free to ask! Here are some follow-up questions you might consider:

1. How would the calculations change if the passing percentage was higher?
2. What would be the effect on A's and B's scores if the total marks were different?
3. How do you calculate percentages of different totals?
4. What happens if B scores exactly the passing marks?
5. Can you provide an example of another scenario using different percentages?

Tip: Always ensure to clearly define your variables when solving word problems to keep track of the relationships.