# How much amount?

$$100\text{ g}$$ of solid $$A$$ of specific heat capacity $$50\text{ J/g}^\circ\text{C}$$ at $$90^\circ\text{C}$$ is placed in a superconducting vessel of mass $$10\text { g}$$ of specific heat capacity $$1\text { J/g}^\circ\text{C}$$. Then some amount of water at $$40^\circ\text{C}$$ is added to the vessel to cool the mixture to $$55^\circ\text{C}$$. Now, the above mixture after cooling down obtains a specific heat capacity of $$25\text{ J/g}^\circ\text{C}$$. Now, to the above mixture is added a solid $$B$$ of specific heat capacity $$20 \text{ J/g}^\circ\text{C}$$ at $$10^\circ\text{C}$$ such that the final temperature of the overall combination becomes $$30^\circ\text{C}$$.

How much amount of solid $$B$$ is added (upto 2 decimal places)?

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