Question

How many time a clock shows angle 90 degree in 1 hour and what time it make an angle 90 degree ?

Answer 1

irst blush it would seem intuitively that 48 is right... each 12 hours it happens twice, once at 15 after and once at a quarter till, times two for the twenty four hour = 48. But that solution has one fault, that as the hours progress, the minute hand lines up 90 degrees later in in the hour. for example the 3:xx alignment at 90 deg happens around 3:33 because the hour hand is already past 90 degrees on the clock face so the minute hand is past the "6". In fact exactly 9:00 the minute hand laps the hour hand, e:g the 7:xx alignment happens at about 7:54 but there is no 8:xx alignment - it actually happens at 9:00. So we only get 11 90-degree alignments per 12 hours. And can double that because of the quarter 'till/quarter past pairs.


your answer depends on the clock ,if it is 3 or 9'o clock then your answer is 1 .

in other hours it is 1