X, Y, Z enter into a partnership. X invests some money money at the beginning. Y invests thrice the amount of X after 4 months and Z invest double the amount of Y after 9 months from the beginning, If the annual gain be Rs 450000, then what is the share of Y?

Rs 200000

The amount and period of investment by X, Y, Z is:

                 X   :   Y   :   Z

Amount      1   :   3   :   6

Time         12  :   8   :   3

         ______________________

Profit share is divided among them on the basis of product of amount and period of investment,

X  : Y  :  Z  = 12 :  24  :  18   =   2  :  4  :  3

 Y's share = $\frac{4}{9}$ x 450000

               =  Rs 200000