A candidate scores 20% and fails by 50 marks, while another candidate who scores 40% marks, gets 30 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination.

Options

A. 500
B. 450
C. 300
D. 400

Answer

To solve the problem step by step, we will follow the information given in the question carefully.

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

### Step 2: Calculate the score of the first candidate
The first candidate scores 20% of the maximum marks. Therefore, the score of the first candidate can be expressed as:
\[ \text{Score of first candidate} = 0.20M \]
According to the problem, this candidate fails by 50 marks. This means that if he had scored 50 more marks, he would have passed. Thus, we can write the equation:
\[ 0.20M + 50 = \text{Minimum passing marks} \]
Let’s denote the minimum passing marks as \( P \):
\[ P = 0.20M + 50 \quad \text{(Equation 1)} \]

### Step 3: Calculate the score of the second candidate
The second candidate scores 40% of the maximum marks. Therefore, the score of the second candidate can be expressed as:
\[ \text{Score of second candidate} = 0.40M \]
This candidate scores 30 marks more than the minimum passing marks, so we can write:
\[ 0.40M = P + 30 \quad \text{(Equation 2)} \]

### Step 4: Set the equations equal to each other
From Equation 1, we have:
\[ P = 0.20M + 50 \]
Substituting this expression for \( P \) into Equation 2 gives:
\[ 0.40M = (0.20M + 50) + 30 \]

### Step 5: Simplify the equation
Now, simplify the equation:
\[ 0.40M = 0.20M + 50 + 30 \]
\[ 0.40M = 0.20M + 80 \]

### Step 6: Solve for \( M \)
Now, we will isolate \( M \):
\[ 0.40M - 0.20M = 80 \]
\[ 0.20M = 80 \]
\[ M = \frac{80}{0.20} \]
\[ M = 400 \]

### Conclusion
The maximum marks for the examination is \( \boxed{400} \).

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