In an examination, a candidate obtains `20%` marks and fails by 75 marks while another candidate obtains `55%` marks and passed by `20%` of the maximum marks. What are the passing marks?

Options

A. A)275
B. B)175
C. C)225
D. D)500

Answer

To find the passing marks based on the information provided, we can follow these steps:

### Step 1: Define Variables
Let the maximum marks be denoted as \( M \).

### Step 2: Express Marks for the First Candidate
The first candidate scores 20% of the maximum marks and fails by 75 marks. Therefore, we can express this as:
\[ \text{Marks obtained by first candidate} = 0.2M \]
Since he fails by 75 marks, we can express the passing marks (denoted as \( P \)) as:
\[ P = 0.2M + 75 \]

### Step 3: Express Marks for the Second Candidate
The second candidate scores 55% of the maximum marks and passes by 20% of the maximum marks. Therefore, we can express this as:
\[ \text{Marks obtained by second candidate} = 0.55M \]
Since he passes by 20% of the maximum marks, we can express the passing marks as:
\[ P = 0.55M - 0.2M \]
This simplifies to:
\[ P = 0.55M - 0.2M = 0.35M \]

### Step 4: Set the Two Expressions for Passing Marks Equal
Now we have two expressions for \( P \):
1. \( P = 0.2M + 75 \)
2. \( P = 0.35M \)

Setting them equal gives:
\[ 0.2M + 75 = 0.35M \]

### Step 5: Solve for Maximum Marks \( M \)
Rearranging the equation:
\[ 75 = 0.35M - 0.2M \]
\[ 75 = 0.15M \]
Now, divide both sides by 0.15 to find \( M \):
\[ M = \frac{75}{0.15} = 500 \]

### Step 6: Calculate Passing Marks \( P \)
Now that we have \( M \), we can find the passing marks:
\[ P = 0.35M = 0.35 \times 500 = 175 \]

### Conclusion
The passing marks are \( \boxed{175} \).

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