A invest \(\frac{1}{8}\)th of the capital for \(\frac{1}{8}\)th of the time, B invest \(\frac{1}{2}\)nd of the capital for \(\frac{1}{2}\)nd of the time and C invest rest of the capital for whole the time. Find profit sharing ratio.

1 : 16 : 24

Let the capital = 8R and the time ratio = 8

                 A     :     B      :       C

Capital :     1     :     4      :       3

Time    :     1     :     4     :       8

------------------------------------------------   

Profit   :     1      :   16     :      24                      (Profit ratio = capital × time)