At what time between 4 and 5 o'clock, will the hands of a watch point in opposite direction?

$54 \frac{6}{11}$ min past 4

At 4'O clock the hands of watches are 20mins spaces apart.

to be in opposite directions, they must be in 30mins

so, min hand will have to gain 50mins spaces.

55min spaces are gained in 60mins.

50min spaces are gained in = (60 \(\div \) 55) x 50 = 54 \frac{6}{11}

Thus, the required time =  54 \frac{6}{11} mins past 4.