In an examination , Vinod scored 25% of marks and failed by 10 marks. Sachin scored 30% of marks. Which were 20 makrs more than the passing marks. Find the total marks of the examination.

Options

A. 500
B. 600
C. 750
D. 800

Answer

To solve the problem, let's denote the total marks of the examination as \( x \).

### Step 1: Determine Vinod's score and passing marks
Vinod scored 25% of the total marks:
\[ \text{Vinod's score} = 0.25x \]
According to the problem, Vinod failed by 10 marks. This means that the passing marks can be expressed as:
\[ \text{Passing marks} = \text{Vinod's score} + 10 = 0.25x + 10 \]

### Step 2: Determine Sachin's score
Sachin scored 30% of the total marks:
\[ \text{Sachin's score} = 0.30x \]
The problem states that Sachin's score was 20 marks more than the passing marks:
\[ \text{Sachin's score} = \text{Passing marks} + 20 \]
Substituting the expression for passing marks from Step 1:
\[ 0.30x = (0.25x + 10) + 20 \]

### Step 3: Simplify the equation
Now, we can simplify the equation:
\[ 0.30x = 0.25x + 30 \]
Subtract \( 0.25x \) from both sides:
\[ 0.30x - 0.25x = 30 \]
\[ 0.05x = 30 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 0.05 to find \( x \):
\[ x = \frac{30}{0.05} = 600 \]

### Conclusion
The total marks of the examination is:
\[ \boxed{600} \]