Solve Question $1$ both $($a$)($b$)$ two parts.

Mr Chan was employed by A Limited as general manager. A Limited is incorporated and carrying on a business in Hong Kong. Mr Chan and the director of A Limited negotiated and signed the employment contract in Jurisdiction X$.$ The employment contract is enforceable in Hong Kong. Mr Chan's remuneration is paid directly into his bank account in Hong Kong. Based on the terms of employment, Mr Chan is required to perform duties in Hong Kong and Jurisdiction X$.$ There is no comprehensive double taxation arrangement signed between Hong Kong and Jurisdiction X$.$ You have been supplied with the following information regarding Mr Chan for the year ended $31$ March $2023$:

$(1)$ Salaries: HK$$1,800,000$

$(2)$ During the year, Mr Chan performed his duties in Jurisdiction $x$ for four months. One$-$third of his salaries was attributable to services performed in Jurisdiction $x$ and was subject to tax in Jurisdiction X$.$ The amount of such tax in Jurisdiction X paid by Mr Chan was HK $$150,000.$

$(3)$ Mr Chan's son aged $15$ is studying full$-$time in an international school in Hong Kong. A Limited signed a contract with the school so that the school fees were payable by A Limited. During the year, A Limited paid total school fees of HK$$127,000$ to the school.

$(4)$ A Limited paid $HK$$$50,000$ to a travel agency to purchase a package tour for Mr Chan and his wife during vacation in December $2022.$ The second$-$hand value of the package tour was HK $$45,000.$

$(5)$ During the year, a flat owned by A Limited was provided to Mr Chan as his residence at a monthly rent of HK$$7,000.$ The market rent of the flat was HK $$21,000$ per month.

$(6)$ On $1$ April $2022,$ A Limited granted options to Mr Chan for the right to acquire $30,000$ shares in A Limited at HK$$5$ each. Mr Chan paid HK$$60,000$ for the options. On $1$ July $2022,$ Mr Chan assigned half of the options to his colleague at a consideration of HK$$70,000.$ On $30$ November $2022,$ Mr Chan exercised the remaining options. On $31$ March $2023,$ Mr Chan sold all the shares obtained from exercising the options. The market prices per share in A Limited were as follows:

$\backslash$table$[[1$ April $2022,$HK$$7],[1$ July $2022,$HK$$9],[30$ November $2022,$HK$$10],[31$ March $2023,$HK$$11]]$

$(7)$ During the year, Mr Chan contributed HK $$30,000$ to a MPF scheme and donated cash of HK $$10,000$ to approved charitable organisations.

$(8)$ During the year, Mr Chan's wife worked as a part$-$time tutor in a tutorial centre in Hong Kong and received salaries of $HK$$$65,000.$

Required:

$($a$)$ Analyse with reasons the locality of Mr Chan's employment with A Limited.

$(5$ marks$)$

$($b$)$ Compute the salaries tax liabilities of Mr Chan and Mrs Chan under joint assessment for the year of assessment $2022/23.$ Ignore provisional tax.

$(20$ marks$)$