Understanding the Problem

The question asks us to find the passing mark as a percentage of the maximum marks. We are given two key pieces of information:

• The student's score is 60% of the maximum marks.
• The student's score is 50% more than the passing mark.

Setting Up Equations

Let's define the variables:

• Let $M$ represent the maximum marks.
• Let $S$ represent the student's score.
• Let $P$ represent the passing mark.

From the given information, we can form the following equations:

1. Student's score in terms of maximum marks: $S = 0.60 × M$
2. Student's score in terms of passing mark: $S = P + (0.50 × P)$, which simplifies to $S = 1.50 × P$

Calculating the Passing Mark Percentage

To find the passing mark ($P$) as a percentage of the maximum marks ($M$), we equate the two expressions for $S$:

$0.60 × M = 1.50 × P$

Now, we solve for $P$ in terms of $M$:

$P = \frac{0.60 \times M}{1.50}$

Simplify the fraction:

$P = \frac{0.60}{1.50} \times M$

$P = \frac{60}{150} \times M$

$P = \frac{6}{15} \times M$

$P = \frac{2}{5} \times M$

Convert the fraction to a decimal:

$P = 0.40 \times M$

This result shows that the passing mark ($P$) is 0.40 times the maximum marks ($M$). Converting the decimal to a percentage:

$P = 40\% \text{ of } M$

Therefore, the passing mark is 40% of the maximum marks.