Three partners shared the profit in 9 : 8 : 10. They invested for 4 months, 6 months and 1 year. What was the ratio of their investments?

81 : 48 : 30

Profit =    Investment × time

Inv. →            x              :             y              :            z

Time  →         4              :             6              :           12

Profit →         9              :              8             :            10

x= \(\frac{9}{4}\)

y = \(\frac{8}{6}\) = \(\frac{4}{3}\)

z =  \(\frac{10}{12}\)  = \(\frac{5}{6}\)

So, x : y : z = \(\frac{9}{4}\) : \(\frac{4}{3}\) : \(\frac{5}{6}\) = \(\frac{81\;:\;48\;:\;30}{36}\)

x : y : z = 81 : 48: 30