Neco 2017 Government Question 10

In a local government council election there are \(30\) seats, of which \(20\) are constituency seats elected by first‑past‑the‑post and \(10\) are list seats used to achieve overall proportionality. Four parties obtain the following numbers of votes: Party X \(85{,}000\), Party Y \(65{,}000\), Party Z \(40{,}000\) and Party W \(20{,}000\). The Hare quota is the total votes divided by the total seats. Using the quota, allocate seats proportionally (initial seats are the integer part of votes/quota, remaining seats are given to the parties with the largest remainders). The constituency results are: Party X wins \(12\) seats, Party Y \(5\) seats, Party Z \(3\) seats and Party W none. List seats are then assigned so that each party's total seats (constituency plus list) equals its proportional entitlement; if a party's constituency seats already exceed its entitlement, it keeps those seats and no list seats are given to it (over‑hang). How many list seats does each party receive, and what is the final seat distribution?