A invest \(\frac{1}{6}\)th of the capital for \(\frac{1}{6}\)th of the time, B invest \(\frac{1}{3}\)rd of the capital for \(\frac{1}{3}\)rd of the time and C invest rest of the capital for whole the time. Find profit sharing ratio.

01 : 04 : 18

Let the capital = 6R and the time ratio = 6

                 A     :     B      :       C

Capital :     1     :     2      :       3

Time    :     1     :     2      :       6  

Profit   :     1      :     4     :      18                      (Profit ratio = capital × time)