Question

3 natural numbers, if the average of 2 numbers is added to the third number then 24,20,18 is obtained, find out all the natural numbers

Answer 1

let the three numbers be a, b,c

case 1: when (a+b)/2 is added to c
[(a+b)/2]+c = 24........................................i

case 2: when (b+c)/2 is added to a
[(b+c)/2]+a = 20........................................ii

case 3: when (c+a)/2 is added to b
[(c+a)/2]+b = 18.......................................iii


adding all the equations, 
[2(a+b+c)]/2 + a+b+c = 62
or, 2(a+b+c) = 62
or, a+b+c = 31

(a+b)/2 + c = 24.............................from i 
(31-c)/2 + c = 24
31+c = 48
c = 17

(c+a)/2 + b = 18 ....................................from iii
(31-b)/2 + b = 18
31+b = 36
b = 5

a = 31-5-17
   =9