In an examination, Karan got `25%` more marks than Sanjay who got `20%` less marks than Mahesh who got `30%` more marks than Anurag. Marks obtained by Karan are what percent more than marks obtained by Anurag?

Options

A. A)`20%`
B. B)`26%`
C. C)`40%`
D. D)`30%`

Answer

To solve the problem step by step, we will define the marks obtained by each student in terms of a variable and then calculate the required percentages.

### Step 1: Define Anurag's Marks
Let Anurag's marks be represented as \( A \).

### Step 2: Calculate Mahesh's Marks
According to the problem, Mahesh got 30% more marks than Anurag. Therefore, Mahesh's marks \( M \) can be calculated as:
\[ M = A + 0.3A = 1.3A \]

### Step 3: Calculate Sanjay's Marks
Sanjay got 20% less marks than Mahesh. Therefore, Sanjay's marks \( S \) can be calculated as:
\[ S = M - 0.2M = 0.8M \]
Substituting \( M \) from Step 2:
\[ S = 0.8 \times 1.3A = 1.04A \]

### Step 4: Calculate Karan's Marks
Karan got 25% more marks than Sanjay. Therefore, Karan's marks \( K \) can be calculated as:
\[ K = S + 0.25S = 1.25S \]
Substituting \( S \) from Step 3:
\[ K = 1.25 \times 1.04A = 1.3A \]

### Step 5: Calculate the Percentage Increase of Karan's Marks over Anurag's Marks
Now we need to find out how much more Karan's marks are compared to Anurag's marks in percentage. The formula for percentage increase is:
\[ \text{Percentage Increase} = \left( \frac{K - A}{A} \right) \times 100 \]
Substituting \( K \) from Step 4:
\[ \text{Percentage Increase} = \left( \frac{1.3A - A}{A} \right) \times 100 = \left( \frac{0.3A}{A} \right) \times 100 = 30\% \]

### Final Answer
Karan's marks are **30%** more than Anurag's marks.

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