A student got 24% marks in an exam and he failed by 56 marks. If he got 60% marks, then his marks are 70 more than the minimum passing marks. What is the maximum marks for the exam?

Options

A. 350
B. 260
C. 380
D. 280

Answer

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

### Step 1: Understand the given information
The student scored 24% of the maximum marks and failed by 56 marks. This means that the minimum passing marks can be expressed as:
\[ \text{Minimum Passing Marks} = 24\% \text{ of } x + 56 \]
This can be written mathematically as:
\[ \text{Minimum Passing Marks} = \frac{24}{100}x + 56 \]

### Step 2: Express the second condition
If the student scored 60% of the maximum marks, he would have scored 70 marks more than the minimum passing marks. This can be expressed as:
\[ \text{Minimum Passing Marks} = 60\% \text{ of } x - 70 \]
This can be written mathematically as:
\[ \text{Minimum Passing Marks} = \frac{60}{100}x - 70 \]

### Step 3: Set the two expressions for minimum passing marks equal to each other
Since both expressions represent the minimum passing marks, we can set them equal:
\[ \frac{24}{100}x + 56 = \frac{60}{100}x - 70 \]

### Step 4: Rearrange the equation
To solve for \( x \), first, let's move all terms involving \( x \) to one side and constant terms to the other side:
\[ 56 + 70 = \frac{60}{100}x - \frac{24}{100}x \]
This simplifies to:
\[ 126 = \left(\frac{60 - 24}{100}\right)x \]
\[ 126 = \frac{36}{100}x \]

### Step 5: Solve for \( x \)
Now, we can isolate \( x \):
\[ x = \frac{126 \times 100}{36} \]
Calculating this gives:
\[ x = \frac{12600}{36} \]
Simplifying further:
\[ x = 350 \]

### Conclusion
The maximum marks for the exam is \( \boxed{350} \).

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