This problem requires calculating the maximum marks of the examination first, and then finding the percentage of marks scored by Girish's friend.

Finding Maximum Marks

Girish scored 441 marks. This score was 75 marks less than 30% of the maximum marks.

1. Calculate the value that represents 30% of the maximum marks:

   $ \text{30\% of Max Marks} = \text{Girish's Score} + 75 $

   $ \text{30\% of Max Marks} = 441 + 75 = 516 \text{ marks} $

2. Calculate the maximum marks (let it be 'M'):

   $ 0.30 \times M = 516 $

   $ M = \frac{516}{0.30} = \frac{5160}{3} = 1720 \text{ marks} $

The maximum marks for the examination are 1720.

Calculating Friend's Marks Percentage

Girish's friend scored 688 marks in the same examination.

1. Calculate the percentage of marks scored by the friend using the maximum marks calculated above:

   $ \text{Friend's Percentage} = \left( \frac{\text{Friend's Score}}{\text{Maximum Marks}} \right) \times 100 $

   $ \text{Friend's Percentage} = \left( \frac{688}{1720} \right) \times 100 $

2. Simplify the fraction:

   $ \frac{688}{1720} = \frac{688 \div 172}{1720 \div 172} = \frac{4}{10} = 0.4 $

   (Alternatively, simplify step-by-step: $ \frac{688}{1720} = \frac{344}{860} = \frac{172}{430} = \frac{86}{215} $. Notice $ 86 = 2 \times 43 $ and $ 215 = 5 \times 43 $. So, $ \frac{2 \times 43}{5 \times 43} = \frac{2}{5} = 0.4 $)

3. Convert the decimal to a percentage:

   $ \text{Friend's Percentage} = 0.4 \times 100 = 40\% $

The percentage of marks scored by Girish's friend is 40%.