a) The first time the town hall clock will chime is at the closest quater hour which is 15 minutes away in regular time. As the clock only gains two minutes per hour, it will take 7.5 hours to gain 15 mins. 12:00pm + 7.5hrs = 19:30pm.
b) Using the same method as part a, the next hour will take the town hall clock 7.5*4 = 30 hours. This will take us to 6:00pm on tuesday. This is the time they will both chime together next on the hour.