Press Association The Barclays Premier League’s bottom side failed to rouse themselves for a must-win game at the Etihad Stadium and seemed condemned after conceding Aguero’s first after just four minutes. Aleksandar Kolarov, James Milner and David Silva also got on the scoresheet as rampant City, who hit the woodwork as well through Wilfried Bony, kept up their challenge for second place with a fourth successive win. But the story of the afternoon was about QPR’s sorry demise after just one season back in the top flight. Questions will now be asked about the future of manager Chris Ramsey and, perhaps more seriously, the status of the club itself with the Football League’s position over their financial situation still unclear. While City’s biggest problem on the day was how to get fit-again Yaya Toure and Vincent Kompany back into the team – both were on the bench – QPR’s sorry day began with administrative issues. It emerged prior to the game that midfielder Sandro had been withdrawn on Home Office advice because of an issue relating to his UK residency visa. Clint Hill, Steven Caulker and Bobby Zamora did at least pass fitness tests but once the game began, it seemed the visitors lacked heart for the battle. Results on Saturday had sent the Londoners to the bottom of the table needing to win to have any hope of survival, but their body language never seemed right. Strikers Zamora and Charlie Austin did look like they could trouble City but the team’s general lack of bite meant they were fighting a lost cause. The writing seemed on the wall in the opening minutes when Leroy Fer gave the ball away and Silva charged through a gap to release Aguero. The Argentinian’s effort was blocked on this occasion but he made no mistake in the fourth minute when he burst through some poor tackling. He did get a lucky rebound off Matt Phillips but his finish from close range was clinical as he expertly dinked over Rob Green. Aguero threatened again but could not quite get the ball under control, Pablo Zabaleta fired across goal, James Milner failed to get away a shot and Fernando drove wide as City dominated. Austin did rattle the crossbar and power a header past Joe Hart as the hosts twice switched off at the back, but the flag was up on both occasions. City doubled their lead when dead-ball specialist Kolarov clipped a free-kick over the wall and beyond Green. Aguero almost added another but Green came out to block. Rangers again showed what they could do if they tried as Fer lobbed a shot onto the bar and Zamora followed up, but City goalkeeper Joe Hart got back to clutch his header. But City’s superiority was never in doubt and they extended their lead after a Yun Suk-young blunder early in the second half. The Korean failed to make a routine interception as Silva sent a long ball forward and Aguero was quick to pounce, racing through on goal and giving Green no chance. Green did react brilliantly to push a Silva shot wide when the Spaniard broke clear soon after but he was soon picking the ball out of the net again as City were awarded a penalty. Silva was bundled over by Phillips as the ball was lofted into the box and referee Mike Dean pointed to the spot. Aguero coolly sent Green the wrong way to complete his hat-trick and take his tally for the season to 31. Things got even worse for QPR – and more embarrassing – as Milner tapped in City’s fifth. Substitute Bony, who replaced the well-acclaimed Frank Lampard, flicked on from a corner and Aguero supplied Milner with an easy finish. Bony himself went close by forcing Green to save with his feet and then hitting the post. Silva completed the humiliation four minutes from time when he took Bony’s backheel in his stride and calmly went round Green. Sergio Aguero scored a hat-trick as QPR slumped to relegation without a whimper in an embarrassing 6-0 defeat at Manchester City.