We know that 1 year = 365.25 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
=> 1 Year = 365.25 x 24 x 60 x 60 Seconds
But 1 billion seconds = ?
1 Year = 365.25 x 24 x 60 x 60 Seconds
? = 1000000000 Seconds
$\mathbf{?}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1000000000}}{\mathbf{365}\mathbf{.}\mathbf{25}\mathbf{}\mathbf{x}\mathbf{}\mathbf{24}\mathbf{}\mathbf{x}\mathbf{}\mathbf{60}\mathbf{}\mathbf{x}\mathbf{}\mathbf{60}}\mathbf{}\mathbf{years}$ = 31. 68 years.
Since at 4 : 20 the minute hand will be at 4 and the angle between them will be same as the distance covered in degree by the hour hand in 20 minutes.
Required angle = distance of hour hand = speed × time = $\frac{1}{2}$× 20 =10 degrees.
At 9 o?clock, the hour hand is at 9 and the minutes hand is at 12, i.e., the two hands are 15 min. spaces apart.
So, the minute hand should gain = (30 - 15) minutes = 15 minutes
55 minutes will be gained in 60 min.
15 minutes spaces will be gained in ((60/55) x 15) min. = 180/11 min.
The hands will be in the same straight line but not together i.e.,in 180 degrees at 180/11 min. past 9.
Angle traced by hour hand in 12 hrs. = 360º.
Angle traced by it in 11/3 hrs= ${\left(\frac{360}{12}*\frac{11}{3}\right)}^{\xb0}$= ${110}^{\xb0}$
Angle traced by minute hand in 60 min. = 360º.
Angle traced by it in 40 min. =(360/60*40) ${\xb0}^{}$=240 ${\xb0}^{}$
Required angle (240 - 110)º = 130º.
In this problem , it has considered that 65 mins = 1hr
So mins has increased by 5 mins so multiply 5 x 24 = 120 mins extra ,
That is now per day it adds 2hr extra, so divide 1440/26 = 59.384 days =~ 60 days.
Since, in one hour, two hands of a clock coincide only once, so, there will be value.
Required time
$T=\frac{2}{11}\left(H\times 30+{A}^{o}\right)$ minutes past H.
Here H - initial position of hour hand = 2 (since 2 O'clock)
A° = Required angle = 0° (Since it coincides)
$T=\frac{2}{11}\left(2\times 30+{0}^{o}\right)$ minutes past 2
=> $\mathbf{1}\frac{\mathbf{10}}{\mathbf{11}}$ minutes past 2
Apply the formula for finding the angle:
Angle=(30h-(11/2)m( where m stands for minutes and h stands for hours)
Hence, 30x11 - 11/2x35 = 330 - 192.5 = 137.5 degrees
The reflex angle = 360 - 192.5 degree = 222.5 degrees.
The total angle traced by the hour hand is the angle traced in 7 hours and 10 minutes.
We know that the angle traced by the hour hand in one hour is 30º and in one minute is 1/2º.
Therefore, (30º x 7) + (10 x 1/2º) = 215º is the angle traced by the hour hand.
For 1 hour, 20 minutes is slower, then for
06 miuntes - 2 minutes is slower
30 minutes - 10 minutes
Actual time | false time
12 12
01 PM 12:40 PM (20 minutes slower)
02 PM 01:20 PM
03 PM 02:00 PM
So, when actual time is 3pm, the false time is 2 pm.
So, it loses 60 minutes when it shows 2 pm.
Comments
There are no comments.Copyright ©CuriousTab. All rights reserved.