In an examination, a student gets 30% marks and failed by 8 marks. In the same exam, another student gets 40% marks and thus he scored 56 marks more than the passing marks then find What could be the maximum mark a student can get in that exam?

Options

A. 520
B. 640
C. 720
D. 450

Answer

To solve the problem step by step, let's denote the maximum marks of the examination as \( M \).

### Step 1: Determine the passing marks
From the problem, we know that:
- A student who scored 30% marks failed by 8 marks.
- Therefore, the passing marks can be expressed as:
\[ \text{Passing Marks} = 30\% \text{ of } M + 8 \]
This can be written mathematically as:
\[ \text{Passing Marks} = 0.3M + 8 \]

### Step 2: Determine the marks of the second student
The second student scored 40% marks and scored 56 marks more than the passing marks. This can be expressed as:
\[ \text{Marks of second student} = 40\% \text{ of } M = \text{Passing Marks} + 56 \]
This can be written mathematically as:
\[ 0.4M = (0.3M + 8) + 56 \]

### Step 3: Simplify the equation
Now we can simplify the equation:
\[ 0.4M = 0.3M + 64 \]
Subtract \( 0.3M \) from both sides:
\[ 0.4M - 0.3M = 64 \]
This simplifies to:
\[ 0.1M = 64 \]

### Step 4: Solve for maximum marks \( M \)
Now, to find \( M \), we divide both sides by 0.1:
\[ M = \frac{64}{0.1} = 640 \]

### Conclusion
Thus, the maximum marks a student can get in that exam is \( \boxed{640} \).

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