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:
Let’s denote the marks obtained by the first student as x and the second student as y.
Since one student secured 9 marks more than the other:
x = y + 9 or y = x + 9 (we’ll consider both cases)
Also, the marks of one student are 56% of the sum of their marks:
x = 0.56(x + y)
Now, substitute y = x + 9 (or x = y + 9) into the equation.
Using y = x + 9:
x = 0.56(x + (x + 9))
x = 0.56(2x + 9)
x = 1.12x + 5.04
-0.12x = 5.04
x = -5.04 / 0.12
x = 42
Now, find y:
y = x + 9
y = 42 + 9
y = 51
However, we should verify the other case (x = y + 9) as well.
Using x = y + 9:
y + 9 = 0.56(y + (y + 9))
y + 9 = 0.56(2y + 9)
y + 9 = 1.12y + 5.04
-0.12y = -3.96
y = 3.96 / 0.12
y = 33
Now, find x:
x = y + 9
x = 33 + 9
x = 42
Both cases yield the same marks for one student (x = 42).
The marks obtained by the two students are 33 and 42.