Edmund's Brainteasers
Problem 17
Problem 17: Saving heat
The Vestry wants to save on the heating bill. They are told that fitting a new boiler would save 45% on the heating bill, putting insulation in the roof would save 30% on the heating bill, and repairing the window frames would save 25% on the heating bill. Since 45 + 30 + 25 =100, it would be nice to think that if all three were done we would save 100% on the heating bill. Of course that can't be right. Assuming the three heat saving methods are independent (which they probably are), what percentage of our heating bill would we save if we adopt all three?