The number of times the hands of a watch are at right angle between 4 p.m. to 10 p.m. is :

In a standard 12-hour clock, the hands form a right angle twice every hour. However, this frequency is reduced during the intervals of 2–4 and 8–10 [t1]. Specifically, while most hours see two right angles, the right angle that occurs exactly at 3:00 and 9:00 is shared between the preceding and succeeding hours [t8]. Between 4 p.m. and 10 p.m., there are 6 hours. For the hours 4–5, 5–6, 6–7, and 7–8, the hands are at right angles 2 times each (8 times total). However, in the 8–10 p.m. period, the hands are at right angles only 3 times instead of 4, because the 9:00 position is a common point for both the 8–9 and 9–10 intervals [t8]. Thus, the total count is 2 + 2 + 2 + 2 + 3 = 11 times [t4][t8].