Neco Model Questions Vol1 2018 Government Question 1

Party X, Y and Z contested a national election for \(360\) seats. Under a first‑past‑the‑post (FPTP) system they won \(120\), \(100\) and \(80\) seats respectively, while the remaining parties shared the rest. The parties' national vote shares were: Party X \(30\%\), Party Y \(25\%\), Party Z \(20\%\), and other parties \(25\%\).\n\n(a) If a proportional representation (PR) system were used, allocating seats strictly in proportion to vote share, how many seats would Party X obtain?\n\n(b) Under which electoral system could Party X achieve a majority (at least \(181\) seats) by allying with the party that has the fewest seats among the three major parties? State the system, the partner party and the total seats of the coalition.