Three partners shared the profit in a business in the proportion of 9 : 8 :11. They invested their capitals for 4 months, 6 months and 18 months, respectively. What was the ratio of their capitals?

81 : 48 : 22

Investment x Time Period = Profit  

                     Investment = \(\frac{Profit}{Time\; Period}\)

                          I  :  II  :  III

Profit                  9  :  8  :  11           

Time Period        4  :  6  :  18  = 2  :  3  :  9

________________________   

 Investment        \(\frac{9}{2}\)  :  \(\frac{8}{3}\)  :  \(\frac{11}{9}\)

                        243  : 144 : 66       = 81 : 48 : 22