Clocks Questions

Angle traced by hour hand in 125/12 hrs = (360/12 * 125/12) = 312102

Angle traced by minute hand in 25 min = (360/60 * 25) = 1500

 Reflex angle = 3600-31212-1500=3600-162102=197102

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.

Time from 7 am to 4.15 pm  = 9 hrs 15 min = 374 hrs 

3 min. 5 sec. of this clock = 3 min. of the correct clock. 

Now 3min.5sec. is37720 hrs of this clock = 3 min.is120 hrs of the correct clock 

374 hrs of clock = 120×72037×374 hrs of the correct clock. 

  = 9 hrs of the correct clock. 

 The correct time is 9 hrs after 7 am. i.e., 4 pm.

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

On straight line means 180 degree angle.
180 = 11/2 min – 30 hrs
180 = 11/2 m – 30 × 3
180 = 11/2 m – 90
(180 + 90) 2 = 11 m
m = 540/11 = 49 1/11 minutes.

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minute, the minute hand gains 330° over the hour hand.

∴ In 16 minutes, the minute hand gain over the hour hand by

Coincide means 00  angle.

This can be calculated using the formulafor time A to B means  [11m/2 - 30 (A)]

Here m gives minutes after A the both hands coincides.

Here A = 3, B = 4

0 =11m/2 –30 × 3
11m = 90 × 2 = 180
m= 180/11 = 16 ⁴/₁₁

So time = 3 : 16 ⁴/₁₁

Angle traced by the hour hand in 6 hours =360o12×6 = 180o.