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. 32%
B. 23%
C. 22%
D. 20%

Answer

To solve the problem step by step, we will define the maximum marks as \( M \) and the passing marks as \( P \).

### Step 1: Set up the equations based on the information given.

1. The first student scores 20% of the maximum marks and fails by 5 marks:
\[ 0.2M + 5 = P \quad \text{(Equation 1)} \]

2. The second student scores 30% of the maximum marks and gets 20 marks more than the passing marks:
\[ 0.3M - 20 = P \quad \text{(Equation 2)} \]

### Step 2: Rearrange the equations to express \( P \).

From Equation 1:
\[ P = 0.2M + 5 \]

From Equation 2:
\[ P = 0.3M - 20 \]

### Step 3: Set the two expressions for \( P \) equal to each other.

\[ 0.2M + 5 = 0.3M - 20 \]

### Step 4: Solve for \( M \).

Rearranging the equation gives:
\[ 5 + 20 = 0.3M - 0.2M \]
\[ 25 = 0.1M \]
\[ M = 250 \]

### Step 5: Substitute \( M \) back into one of the equations to find \( P \).

Using Equation 1:
\[ P = 0.2(250) + 5 \]
\[ P = 50 + 5 = 55 \]

### Step 6: Calculate the passing percentage.

The passing percentage is calculated as:
\[ \text{Passing Percentage} = \left(\frac{P}{M}\right) \times 100 \]
\[ \text{Passing Percentage} = \left(\frac{55}{250}\right) \times 100 = 22\% \]

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

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