A clock was set right at 12 noon. At a true time of 3:00 p.m. it showed 3:20, as on the right. It gains at a steady rate. What is the true time when this clock shows 9:00 p.m.?

In 3 true hours the clock moves 3 h 20 min, i.e. 200 clock-minutes per 180 true minutes. When it shows 9:00 p.m. it has moved 540 clock-minutes, so the true time passed is $540\times 180÷200=486$ min = 8 h 6 min: 8:06 p.m. (8:00 p.m. subtracts 20 min per 3 clock hours, i.e. 60 min; 8:40 p.m. subtracts only 20 min.)