Assume that a database stores a set of intervals, each of which defines start and end points, a weight and a type. Typed intervals enrich the data representation and support applications involving different kinds of data intervals. Given a query time and type, the system reports k intervals that intersect the time, contain the type and have the largest weight. We develop a new structure to manage typed intervals based on the standard interval tree and propose efficient query algorithms. Experiments with synthetic datasets are conducted to verify the performance advantage of our solution over alternative methods.