Question

divide 184 into two parts such that 1/3th of one part exceed 1/7th of the other part by 8

Answer 1

Let the two parts be x and y

x + y = 184 

Also , 

x/ 3 = 8 + (y/7)
x = 24 + 3y/ 7 

24 + 3y/7  + y = 184 

10y / 7 = 160 

y / 7 = 16

y = 112 

x = 72

Answer 2

let the parts be x and y
x + y = 184 ---> x + y - 184 = 0 ___(i)
x/3 = y/7 + 8 ---> x/3 - y/7 - 8 = 0 ___(ii)
(ii)×7: 7x/3 - y - 56 = 0
(i) + (ii): (x + y - 184) + (7x/3 - y - 56) = 0
10x/3 - 240 = 0
10x/3 = 240
10x = 80
x = 8