How many times, the hands of a clock will be at 30° with each other in a day?
(A) 36 (B) 40 (C) 44 (D) 48 (E) 42
Answers
Given: How many times, the hands of a clock will be at 30° with each other in a day?
Find: How many times. the hands of a clock will be at 30° with each other in a day.
• Every hour, there are two possibilities for the clock hands to be at 30 degrees with each other. You have the option of having the long hand 30 degrees to the left of the short hand, and later having the long hand 30 degrees to the right of the short hand. It happens twice more in the next hour. So two times an hour.
• Then there's the question of how to define "a day." Is it 24 hours, 12 hours, from sunrise to sunset.
• If you define a day as beginning at sunrise and ending at sunset, it becomes very difficult to answer the question – you would have to tell us what day of the year it is.
• If this is the case, the answer will be: 2 x 24 = 48 times.
• Now, 30 degrees is one-twelfth of a 360-degree circle, so there are 30 degrees between 12 and 1, 30 degrees between 1 and 2, and so on.
• And if the day is defined as 24 hours, you'll get 48 times per day.
• If the day is defined as 12 hours, you will get 2 x 12 = 24 times per day.
• It's worth noting that the clock rotates one full circle (for the short clock hand) every 12 hours. So, if the day is defined as 24 hours, the short hand will go two circles.
• The answer is 48 times per day.
• if you consider 24 hours and 24 times per day if you consider 12 hours.
The option D) 48 is correct answer.