Two students appeared at an examination. One of them secured 15 marks more than the other and his marks were 55% of the sum of their marks. The marks obtained by them are:

Correct option is C

Given:
Among two students one of them secured 15 marks more than the other and his marks were 55% of the sum of their marks.
Solution:
Let, one of them scored x
Then the score of the other student is (x + 15)
Sum of their marks = (x + x + 15) = (2x + 15)
Accordingly,
​$$(x + 15) = \left(\frac{55}{100}\right) \times (2x + 15) \\\implies 20 \times (x + 15) = 11 \times (2x + 15) \\\implies 20x + 300 = 22x + 165 \\\implies (22x - 20x) = (300 - 165) \\\implies 2x = 135 \\\implies x = 67.5\\$$​​
The number secured by the one student = 67.5 
The number secured by the other student = 67.5 + 15 = 82.5