Question

How to find three positive numbers who are in the ratio 1/2:1/3:1/4 and sum or their square is 244?

Answer 1

Given ratio = 1/2 : 1/3 :1/4 = 12/2:12/3:12/4[multiplying each by 12]

      = 6:4:3

Let the numbers be 6x, 4x and 3x.

Now,

(6x)²+(4x)²+(3x)²=244

36x²+16x²+9x²=244

61x²=244

x²=24/61=4

x=2(as x is positive we neglect -2)

Numbers = 6 x 2=12,   4 x 2=8    and    3 x 2=6