Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

Given

• Two students' marks differ by 9
• The higher mark is 56% of the sum of their marks

Let the marks be
Higher = x, Lower = y, with x = y + 9Also given: x = 56% of (x + y) ⇒ x = 0.56(x + y)

Solve the System
x = 0.56x + 0.56y ⇒ 0.44x = 0.56yx = (0.56/0.44) y = (56/44) y = (14/11) yBut x = y + 9 ⇒ (14/11) y = y + 9(14/11 − 1) y = 9 ⇒ (3/11) y = 9 ⇒ y = 33x = y + 9 = 42

Check

• Sum = 42 + 33 = 75; 56% of 75 = 42 ✓

Final Answer
Marks obtained = 42 and 33.