UPSC 2016 CDS I Math Paper

Let the ages of the three brothers be x years, y years and z years.
x+y=4....(1)
y+z=6....(2)
z+x=8....(3)
Adding (1), (2) and (3), we have
2(x+y+z)=18
⇒x+y+z=9...(4)
From (1) and (4), we have
4+z=9
⇒z=5
Similarly, y = 1 and x = 3Therefore, age difference between the eldest and the youngest = 5 – 1 = 4 years
Trick :
Students are advised to think3 numbers such that the sums of two of them at a time are 4 years, 6 years and 8 years.
Such numbers are 1, 3 and 5