A candidate who scores 30% fails by 5 marks, while another candidate who scores 40% marks gets 10 more than minimum passing marks. The minimum marks required to pass are:

Options

A. 50
B. 100
C. 45
D. 150

Answer

To solve the problem, we need to determine the minimum marks required to pass (let's denote this as \( P \)) based on the information given about the two candidates.

### Step 1: Set up the equations based on the candidates' scores

1. **Candidate 1**: This candidate scores 30% and fails by 5 marks.
- This means the score of Candidate 1 can be expressed as:
\[ 0.30X = P - 5 \]
- Here, \( X \) is the total marks.

2. **Candidate 2**: This candidate scores 40% and gets 10 marks more than the minimum passing marks.
- This means the score of Candidate 2 can be expressed as:
\[ 0.40X = P + 10 \]

### Step 2: Solve the equations

Now we have two equations:
1. \( 0.30X = P - 5 \) (Equation 1)
2. \( 0.40X = P + 10 \) (Equation 2)

We can rearrange both equations to express \( P \) in terms of \( X \).

From Equation 1:
\[ P = 0.30X + 5 \]

From Equation 2:
\[ P = 0.40X - 10 \]

### Step 3: Set the equations for \( P \) equal to each other

Since both expressions equal \( P \), we can set them equal to each other:
\[ 0.30X + 5 = 0.40X - 10 \]

### Step 4: Solve for \( X \)

Now, we will solve for \( X \):
1. Rearranging gives:
\[ 5 + 10 = 0.40X - 0.30X \]
\[ 15 = 0.10X \]
2. Dividing both sides by 0.10:
\[ X = \frac{15}{0.10} = 150 \]

### Step 5: Substitute \( X \) back to find \( P \)

Now that we have \( X = 150 \), we can substitute it back into either equation to find \( P \). Let's use Equation 1:
\[ P = 0.30(150) + 5 \]
\[ P = 45 + 5 = 50 \]

### Conclusion

The minimum marks required to pass are \( \boxed{50} \).

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