In an examination, a student who gets 20% of the maximum marks fails by 5 marks. Another student who scores 30% of the maximum marks gets 20 marks more than the pass marks. The necessary percentage required for passing is

Options

A. A) 32
B. B) 23
C. C) 22
D. D) 20

Answer

To solve the problem step-by-step, we will denote the maximum marks as \( M \).

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

### Step 2: Determine the marks scored by Student A
Student A scores 20% of the maximum marks:
\[ \text{Marks scored by A} = 0.2M \]
According to the problem, Student A fails by 5 marks, which means the passing marks \( P \) can be expressed as:
\[ P = 0.2M + 5 \]

### Step 3: Determine the marks scored by Student B
Student B scores 30% of the maximum marks:
\[ \text{Marks scored by B} = 0.3M \]
It is given that Student B scores 20 marks more than the passing marks, so we can write:
\[ 0.3M = P + 20 \]

### Step 4: Set the equations equal to each other
Now we have two equations for \( P \):
1. \( P = 0.2M + 5 \)
2. \( P = 0.3M - 20 \)

We can set these two equations equal to each other:
\[ 0.2M + 5 = 0.3M - 20 \]

### Step 5: Solve for \( M \)
Rearranging the equation gives:
\[ 5 + 20 = 0.3M - 0.2M \]
\[ 25 = 0.1M \]
Dividing both sides by 0.1:
\[ M = 250 \]

### Step 6: Find the passing marks \( P \)
Now substituting \( M \) back into one of the equations for \( P \):
\[ P = 0.2M + 5 = 0.2(250) + 5 = 50 + 5 = 55 \]

### Step 7: Calculate the percentage required for passing
To find the necessary percentage required for passing, we calculate:
\[ \text{Percentage required} = \left(\frac{P}{M}\right) \times 100 = \left(\frac{55}{250}\right) \times 100 \]
Calculating this gives:
\[ \text{Percentage required} = \left(\frac{55}{250}\right) \times 100 = 22\% \]

### Final Answer
The necessary percentage required for passing is **22%**.

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