UPSC CDS 2 2021 Math Paper

Given, the ratio of three positive numbers is 2:3:5.
Let three numbers be 2a,3a and 5a.
According to the question,
(2a)2+(3a)2+(5a)2‌‌=1368
⇒4a2+9a2+25a2‌‌=1368
⇒‌38a2‌‌=1368
⇒‌a2=‌

1368

38

‌‌=36
⇒‌a‌‌=6
The numbers are 2×6,3×6 and 5×6
i.e., 12, 18 and 30 .
Sum of the numbers
=12+18+30=60
Hence, sum of the numbers is 60 .