General Questions

Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.

Now 23 hrs 44 min. of this clock = 24 hours of correct clock.

∴ (356/15) hrs of this clock = 24 hours of correct clock

89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.

= 90 hrs of correct clock.

So, the correct time is 11 p.m.

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 )

i.e., 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°

Time from 12 p.m. on Tuesday to 2 p.m. on the following Tuesday = 7 days 2 hours.

= 170 hours.

The watch gains = (2 + 4 x 4/5) min

= 34/5 min. in 170 hrs.

Now, 34/5 min are gained in 170 hrs.

Then, 2 min are gained in (170 x 5/34 x 2) hrs.

Watch is correct after 2 days 2 hrs after 12 p.m. on Tuesday, i.e., it will be correct at 2 p.m. on Thursday.

One hour = 60 min

∴ 18/60 = 3/10

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

Angle between hands of a clock

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

=> 30(H − M/5) + M/2 degrees

Here H = 4, M = 15 and the minute hand is behind the hour hand.

Hence the angle
= 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

As minute hand covers, 60 degrees

Minute hand covers (4800/60)° = 80°

For ticking 6 times, there are 5 intervals.

Each interval has time duration of (30/5) = 6 secs

At 12 o'clock, there are 11 intervals,
so total time for 11 intervals =(11 x 6)= 66 secs.

Angle traced by the hour hand in 6 hours

=		360	x 6		º	= 180º
		12

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.