Two students appeared for an examination. One of them secured 24 marks more than the other and his marks were $65\%$ of the sum of their marks. The marks obtained by them are ______.

Let the marks obtained by the two students be $x$ and $x+24$.The sum of their marks is:
$$\text{Sum}=x+(x+24)=2x+24$$
According to the question, the higher marks ($x+24$) is $65\%$ of the sum of their marks:
$$x+24=\frac{65}{100}(2x+24)$$
$$x+24=\frac{13}{20}(2x+24)$$
Multiply both sides by 20 to clear the fraction:
$$20(x+24)=13(2x+24)$$
$$20x+480=26x+312$$
$$480-312=26x-20x$$
$$168=6x$$
$$x=\frac{168}{6}=28$$
So, the marks obtained by the students are:Lower marks: $x=28$$Highermarks:$ x + 24 = 28 + 24 = 52
$$
Thus, the marks are 52 and 28.