Three partners shared the profit in a business in the ratio of 8 : 12 : 20 . They invested the capital for 3 months , 4 months , and 5 months . What was the ratio of their capitals?

8 : 9 : 12

Profit = Investment × time

                  I   :    II     :     III

Time    ⇒   3   :     4     :     5

Profit   ⇒   8  :     12     :     20

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Inv.     ⇒    \(\frac{8}{3}\)  :   \(\frac{12}{4}\)    :   \(\frac{20}{5}\)

           = \(\frac{8}{3}\) : 3 : 4 = 8 : 9 : 12

[*Inv. Ratio  = \(\frac{Profit\;ratio}{Time.\;ratio}\)]