Correct option is A
Given:
After 12:00:00 the hour hand and minute hand of a clock will be perpendicular to each other for the first time
Solution:
After 12:00, the first time the hour and minute hands of a clock are perpendicular, or form a 90-degree angle, is at approximately 1:05.
Let me explain why that is:
Both the hour and the minute hand start off at 12:00 (with "0" degrees between them).
Every minute, the minute hand moves 6 degrees (as 360 (full circle) divided by 60 (minutes) equals 6 (degrees every minute)), and the hour hand moves 0.5 degrees (as 360 (full circle) divided by 12 (hours) divided by 60 (minutes) yields 0.5 (degrees every minute)).
So, for the angle between both hands to be 90 degrees, the difference in their positions must be 90 degrees. If "M" stands for the number of minutes passed, the equation is:
6M - 0.5M = 90
Solving for M (the number of minutes after 12:00), we get:
5.5M = 90 --> M = 90/5.5 ≈ 16.36 minutes,
which is close to 16 minutes and 21 seconds.
