Clocks Questions with Solutions

Clock questions ask about the angle between the hour and minute hands at a given time, or the times at which the hands are together, opposite each other or at right angles. The key facts are that the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute, so the minute hand gains 5.5 degrees on the hour hand every minute. The angle between the hands at H hours and M minutes is |30H - 5.5M| degrees. In 12 hours, the hands coincide 11 times, are opposite 11 times, and are at right angles 22 times. The topic also covers faulty clocks that gain or lose time, and mirror images of clocks. Learning these few formulas turns most clock questions into short calculations. Practise the clock questions below, each with a step-by-step solution.