In an examination, a student who scores 25% of the maximum marks fails by 30 marks. Another student who scores 50% of the maximum marks gets 20 marks more than the minimum pass marks. What are the max

Let $M$ be the maximum marks for the examination.
Let $P$ be the minimum required marks to pass the examination.

According to the problem, Shubhendu scores 25% of $M$ and fails by 30 marks. This means his score is $P - 30$.

$$0.25M = P - 30 \quad (1)$$

Another candidate scores 50% of $M$ and gets 20 marks more than the minimum required marks. This means his score is $P + 20$.

$$0.50M = P + 20 \quad (2)$$

From equation (1):

$$P = 0.25M + 30$$

From equation (2):

$$P = 0.50M - 20$$

Since both expressions equal $P$, we can set them equal to each other:

$$0.25M + 30 = 0.50M - 20$$

Subtract $0.25M$ from both sides:

$$30 = 0.25M - 20$$

Add 20 to both sides:

$$30 + 20 = 0.25M$$ $$50 = 0.25M$$

Divide by 0.25:

$$M = \frac{50}{0.25}$$ $$M = 50 \times 4$$ $$M = 200$$

The maximum marks for the examination is 200.

The final answer is $\text{200}$.