At what time between 5:30 and 6 O'clock, will the hands of a clock be at right angle ?
5:30 से 6 बजे के बीच किस समय घड़ी की सूइयाँ समकोण पर होंगी?

Options

A. `43(3)/(11)` min past 5
B. `43(7)/(11)` min past 5
C. 40 min past 5
D. 45 min past 5

Answer

B

Explanation

At 5, both the hands are 25 min apart and to be at right angle both the hands have to be 15 min apart as shown in Fig. (ii) and Fig. (iii). Since, we have to take the position of clock between 5:30 and 6 O.clock, therefore the positions of hands of clock as above Fig. (iii) is our answer.
Now, it is clear from Fig. (i) and Fig. (iii) that minute hand needs to travel (25 + 15) = 40 min space in order to form a right angle with the hour hand. 55 min space is gained in 60 min. Therefore, 40 min spaces will be gained in `((60)/(55) xx 40)` min or `43(7)/(11)` min. Therefore, the hands are at right angle at `43(7)/(11)` min past 5.