How much watch gain or lose per day, If its hands coincide every 64 min’s
55min spaces are covered in 60min
60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.
loss in 64min=(65+5/11)- 64 =16/11
Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon
Angle traced by the hour hand in 6 hours=(360/12)×6
At what time between 7 & 8 o'clock will the hands of a watch be in the straight line but no together
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.At 7 o'clock, they are 25 min. spaces apart.Minute hand will have to gain only 5 min. spaces.55 min. spaces are gained in 60 min.
5 min spaces are gained in min = min
so, Required time = min past 7
At what time between 5.30 & 6 will the hands of a watch be at right angle
At 5 o'clock, the hands are 25 min. spaces apart.To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min
40 min. spaces are gained in 60/55×40 min = 43 7/11 min.
At what time between 9&10 will the hands of a watch be together?
To be together between 9 and 10 o’clock, the minute hand has to gain 45 min.
spaces. 55 min. spaces gined in 60 min.
45 min. spaces are gained in [60 / 55 × 45] min. or 49 1/11 min. The hands are together at 49 1/11 min. past 9.
At what time between 4 & 5 will the hands of a watch point in opposite directions
4 o'clock, the hands of the watch are 20 min. spaces apart.To be in opposite directions, they must be 30 min. spaces apart. Minute hand will have to gain 50 min. spaces.55 min. spaces are gained in 60 min
50 min. spaces are gained in min. or
Required time = min. past 4.
How many times in a day the hands of a clock are straight
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.
How much does a watch lose per day, if its hands coincide every 64 minutes
The minute hand of a clock overtakes the hour hand at intervals of M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.
Here M = 64. The clock gains or losses in a day by
=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)
=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.
How many times are the hands of a clock at right angles in a day
In a 12 hour period, the minute hand makes 12 revolutions while the hour hand makes one. If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times. In a 24 hour day you get 2×22=44.
How many times do the hands of a clock coincide in a day
The hands of a clock coincide 11 times in every 12 hours
(Since between 11 and 1, they coincide only once, i.e. at 12 o'clock). The hands coincide 22 times in a day.
