Sunil gets `10%` more marks than Akbar .What percentage of marks does Akbar get less than Sunil ?

Options

A. `9 %`
B. `10 %`
C. `9(1)/(11)%`
D. `11 (1)/(9)%`

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Understand the relationship between Sunil's and Akbar's marks
We know that Sunil gets 10% more marks than Akbar. Let's denote Akbar's marks as \( A \).

### Step 2: Express Sunil's marks in terms of Akbar's marks
Since Akbar's marks are \( A \), Sunil's marks will be:
\[ S = A + 10\% \text{ of } A = A + \frac{10}{100} \times A = A + 0.1A = 1.1A \]
So, Sunil's marks \( S \) can be expressed as \( S = 1.1A \).

### Step 3: Calculate how much less Akbar's marks are compared to Sunil's marks
We need to find out what percentage of Sunil's marks Akbar's marks are less. The difference in marks between Sunil and Akbar is:
\[ \text{Difference} = S - A = 1.1A - A = 0.1A \]

### Step 4: Calculate the percentage decrease
To find the percentage decrease of Akbar's marks compared to Sunil's marks, we use the formula:
\[ \text{Percentage decrease} = \left( \frac{\text{Difference}}{\text{Sunil's marks}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage decrease} = \left( \frac{0.1A}{1.1A} \right) \times 100 \]

### Step 5: Simplify the expression
The \( A \) in the numerator and denominator cancels out:
\[ \text{Percentage decrease} = \left( \frac{0.1}{1.1} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage decrease} = \frac{0.1 \times 100}{1.1} = \frac{10}{1.1} \approx 9.09\% \]

### Conclusion
Thus, Akbar gets approximately \( 9.09\% \) less marks than Sunil.

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