Question

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

Answer 1

The answer is precisely 54 6/11th minute past 4.

The numerical calculation is as follows:-

The hands of the watch are 20 min. spaces apart at 4 O'clock.

So, to be in opposite directions, they must be 30 min. spaces apart.

This means minute hand will have to gain 50 min. spaces.

As 55 min. spaces are gained in 60 min. ,

=>50 min. spaces are gained in 60/55 x 50 min. or 54 6/11 min.

Hence, required time = 54 6/11 min. past 4.