Two students appeared at an examination. One of them secured 9 marks more than…
2024
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks. The marks obtained by them are:
- A.
39,30
- B.
41,32
- C.
42,33
- D.
43,34
Attempted by 23 students.
Show answer & explanation
Correct answer: C
Let the marks be (x + 9) and x.
Condition: the higher mark equals 56% of the sum of the two marks.
Set up the equation: x + 9 = (56/100) * ((x + 9) + x)
Multiply both sides by 100: 100(x + 9) = 56(2x + 9).
Simplify by dividing both sides by 4: 25(x + 9) = 14(2x + 9).
Expand: 25x + 225 = 28x + 126.
Rearrange: 225 - 126 = 3x, so 99 = 3x and x = 33.
Therefore the marks are x + 9 = 42 and x = 33. Check: sum = 75 and 56% of 75 = 42, which matches the larger mark.
Answer: 42 and 33