Course Name: Quant Interview Questions Preparation, Section No: 2, Unit No: 9, Unit type: Quiz
You have hour 1 through hour 12 twice per day, where the hands will be at right angles (For example: 12:15 and 12:45, 5:15 and 5:45 so on…). So, it is 24 times each half day, and it means 48 times in a given day. Why are you skipping one hour?
At first, intuitively it seems like the answer would be 48, as during each hour the hands are at right angles twice. So 24 times in a 12 hr period and 48 over the entire day. However, there is a small catch.
Let's look at the hours 2 to 3. The first time the hands would be at 90 degrees is just after 2:25 and then the next time they would be at 90 degrees is at exactly 3 o'clock. Now, during the hour 3 to 4, there will only be one 90 degrees period and this would be just after 3:30.
Similarly looking at hours 8 to 9. 90 degrees will be at around 8:25 and then at exactly 9 o'clock. Then during the hour 9 to 10, once again there will be only one 90 degree period at around 9:30.
Hence, in case of 3 o'clock and 9 o'clock, a right angle happens only once. Therefore only 22 right angles in a 12 hour period and over the entire day, there will be only 44 right angles.