UPSC CDS I 2019 Math Paper

Let the three numbers be a, a + 36 and b
a+a+36+b=100
⇒2a+b=64…..(1)
The only possible value for b is 2 as any other prime value of b will give fractional value of a.
Thus, putting b=2 in (1), we get:
2a=62⇒a=31
Thus, the numbers are 31, 67 and 2.