Divide 243 kg weight in three parts such that half of the first part, one-third of the second part and one-fourth of the third part are equal.

54 kg, 81 kg, 108 kg

let the numbers = x, y , z

So \(\frac{1}{2}\) x = \(\frac{1}{3}\) y = \(\frac{1}{4}\) z = k

x = 2k , y = 3k , z = 4k

x + y + z = 243

2k + 3k + 4k = 243

9k = 243

k = 27

So numbers are x = 54 , y = 81 , z = 108