$($A$)$ Inc. has decided to purchase $100\%$ of the voting shares of $($B$)$ Ltd$.$ for

$$825,000$ in cash on July $1,2022.$ On the date just prior to the acquisition, the

balance sheets of each of these companies were as follows:

On that date, the fair values of $($B$)$ Ltd$.$ assets and liabilities were as follows:

In addition to the above, an independent appraiser determined that $($B$)$ Ltd$.$ had

trademarks with a fair market value of $$180,000$ which had not been reported on its

balance sheet. In addition, $($A$)$ Inc.$\text{'}$s fair market values were equal to their book

values with the exception of the Company's inventory and plant and equipment,

which were said to have fair values of $$30,000$ and $$480,000,$ respectively.

Based on the information provided:

a$)$ Calculate the amount of goodwill arising from this combination.