Three partners shared the profit in a business in the ratio of 10 : 12 : 13 . They invested the capital for 2 months, 6 months, and 5 months. What was the ratio of their capitals?

15 : 6 : 13

Profit = Investment × time

                  I   :    II     :     III

Time    ⇒   2   :     6     :     3

Profit   ⇒   10  :     12     :     13

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Inv.     ⇒    \(\frac{10}{2}\)  :   \(\frac{12}{6}\)    :   \(\frac{13}{3}\)

           = 5 : 2 :  \(\frac{13}{3}\) = 15 : 6 : 13

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