At what time between 4 and 5 o' clock will the hands of a clock be at right angle?
Answer: B
At 4 o' clock, the minute hand is 20 minute spaces behind the hour hand.
Now, when the two hands are at right angles, they are fifteen min spaces
apart. So, they are at right angles in following two cases.
Case I ? When the minute hand is 15 min spaces behind the hour hand.
In this case, min hand will have to gain (20-15) = 5 min spaces.
= (60/55)*5 = 60/11
∴ They are at right angle at 60/11 minutes past 4.
Case II ? When the minute hand is 15 minute spaces ahead of the hour hand.
In this case the minute hand will have to gain (20+15) = 35 min spaces.
= (60/55)*35 = 420/11 min
∴ They are at right angles at 420/11 min past 4.
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What will be angle between the two hands of a clock at 10.25 pm?
Answer: C
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Find the angle between the hour hand and the minute hand of a clock when the time is 3.25
Answer: A
At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.
Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°
Hence, Angle between Hour and the Minute hand = ( 60 - 12.5 ) = 47.5°
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An accurate clock is started at noon. By 10 minutes past 3, the hour hand has turned through:
Answer: B
At 3 o’ clock, the hour hand is at 90 degrees from the vertical.
In 10 minutes,
Hour hand = 90 + 10 x (0.5) = 95 (The hour hand moves at 0.5 dpm)
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The two hands of a clock will be together between h and (h+1) o'clock at
Answer: A
At h o' clock, the minutes hand is 5 h minute spaces
behind the hour hand.
The minute hand gains 55 min spaces in 60 mins.
∴ The minute hand will gain 5h minute spaces
in 60/55 * 5h = 60h/11 minutes.
∴ The two hands will be together between
'h' and 'h+1' o' clock at (60/11)h minutes h o' clock.
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At what time between 7 o'clock and 8 o'clock, will the hands of a clock be together?
Answer: B
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How many times in a day, are the hands of a clock in straight line but opposite in direction?
Answer: B
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
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At what angle the hands of a clock are inclined at 40 minutes past 2?
Answer: B
At 2 o’ clock, the hour hand is at 60° from the vertical.
In 40 minutes,
Hour hand = 60 + 40 x (0.5) = 80° (The hour hand moves at 0.5 dpm)
Minute hand = 40 x (6) = 240° (The minute hand moves at 6 dpm)
Difference or angle between the hands = 240 - 80 = 160°
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The angle between the minute hand and the hour hand of a clock when the time is 8.30, is
Answer: B
At 8 o’ clock, the hour hand is at 240 degrees from the vertical.
In 30 minutes,
Hour hand = 240 + 30 x (0.5) = 240 + 15 = 255 (The hour hand moves at 0.5 dpm)
Minute hand = 30 x (6) = 180 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 255 - 180 = 75 degrees
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Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together ?
Answer: B
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