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

Options

A. a. 45 min past 4
B. b. 40 min past 4
C. c. `50(4)/(11)` min past 4
D. d. `54(6)/(11)` min past 4

Answer

D

Explanation

At 4 O. clock tha hands are 20 min apart from each other and for having in the opposite direction they needs to be 30 min apart.
From fig (i) and Fig (ii), it is clear that minute hand has to travel
(20 + 30) min space in order to be in opposite direction of each other.
Now, 55 min space is gained in 60 min
Therefore, 50 min space will be gained in `((60)/(55) xx 50)` min or `54(6)/(11)` min.
Hence, the hands of the clock will be in opposite direction at `54(6)/(11)` min past 4.