How many times are the hands of a clock at right angle in a day?

A. 22
B. 24
C. 44
D. 48

• Ans)C (44)
  In 12 hr's the hands of the clk will be right angle for 22 times..
  as in 1 hr time the hands of the clk will be right angle fot 2 times.
  but in (11'o clk - 1'o clk) time it will right angle only twice(2).
  so for 12 hrs time 22 times it will be right angle.
  for 24 hrs time 44 times it will be right angle..
  
• 11 years agoHelpfull: Yes(8) No(6)
• Option C
  44 times
  
• 12 years agoHelpfull: Yes(3) No(3)
• The minute hand moves at a faster rate of 5.5 degrees a minute (because the hour hand moves 0.5 degrees a min and the minute hand moves 6 degrees a minute).
  
  so the difference in degree is 6 - 5.5 degree ...
  
  We start at 12 midnight. The hands are together. For subsequent 90 degree angles to occur, the minute hand must "overtake" the hour hand by
  90 degrees, then 270 degrees, then 360 + 90 degrees, then 360 + 270 degrees, then 360 + 360 +90 degrees.. and so on.
  
  This can be re-expressed as: (1)90, 3(90), 5(90), 7(90), 9(90), 11(90)... n(90).
  The number of minutes this takes to happen can be expressed as (1)90/5.5, 3(90)/5.5, 5(90)/5.5, 7(90)/5.5, 9(90)/5.5, 11(90)/5.5... n(90)/5.5.
  
  In one day, there are 24 hr * 60 mins = 1440mins
  To find the maximum value of n,
  n(90)/5.5 = 1440
  n = 88
  
  but as seen from above, n must be an odd number (by pattern recognition and logic)
  hence n must be the next smallest odd number (87)
  counting 1,3,5,7,9,11......87, we see that the number of terms = (87-1)/2 +1 = 44.
  
  In other words, the minute hand "overtakes" the hour hand on 44 occasions in 24 hours in order to give a 90 degree angle.
  Therefore the answer to your question is 44.
• 10 years agoHelpfull: Yes(3) No(0)
• C.44
  In 24 Hours They Are At Right Angles 44 Times
• 10 years agoHelpfull: Yes(0) No(0)
• the hands will be at right 2 times in one hour. hence 24 x 2 = 48 is the answer.
• 7 years agoHelpfull: Yes(0) No(0)