How much amount?

100 g100\text{ g} of solid AA of specific heat capacity 50 J/gC50\text{ J/g}\, ^\circ\text{C} at 90 C90\ ^\circ\text{C} is placed in a superconducting vessel of mass 10 g10\text { g} of specific heat capacity 1 J/gC1\text { J/g}\, ^\circ\text{C}. Then some amount of water at 40 C40\ ^\circ\text{C} is added to the vessel to cool the mixture to 55 C55\ ^\circ\text{C}.

Now, the above mixture after cooling down obtains a specific heat capacity of 25 J/gC25\text{ J/g}\, ^\circ\text{C}. Then, to the above mixture is added a solid BB of specific heat capacity 20 J/gC20 \text{ J/g}\, ^\circ\text{C} at 10 C10\ ^\circ\text{C} such that the final temperature of the overall combination becomes 30 C30\ ^\circ\text{C}.

How much amount of solid BB is added (up to 2 decimal places)?

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