When will the hands of a watch point exactly in opposite directions between 3 o'clock and 4 o'clock?
At 3 o'clock, the hands of the watch are 15 min spaces apart. To be in opposite directions, they must be 30 min spaces apart. For that, the minute hand will have to gain 45 min spaces over the hour hand. The minute hand gains 55 min space over the hour hand in 60 min. ∴ The minute hand gains 50 min space over the hour hand in (45 * 60/55) min or 49 1/11 min. ⇒ Required time = 49 1/11 min past 3.
