Aptitude - Clock - Discussion

Explain every lines in detail:

In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.

In every hour, both the hands coincide once.

The hands are in the same straight line when they are coincident or opposite to each other.

When the two hands are at right angles, they are 15 minute spaces apart.

When the hands are in opposite directions, they are 30 minute spaces apart.

Angle traced by hour hand in 12 hrs = 360°.

Angle traced by minute hand in 60 min. = 360°.

If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast.

On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

So, in 1 hour minute hand covers 360 degrees.

So, in 1 hour Hour hand completes 30 degrees. (Since clock has 12 hours in a complete journey.

So 12 hours = 360 degrees that means 360/12 = 30 degrees in 1 hour.

Now, the solution is straightforward.

1 hour Hour hand traverses 30 degrees.

So, in 6 hours it will traverse = 30*6 = 180 degrees. :).

A Clock strikes every hour-once at 1.00, twice at 2.00, and so on. The clock takes 6 seconds to strike 5.00 and 12 seconds to strike 9.00. the time needed to strike 1.00 is negligible. How long does the clock need for all its striking in 24 hours?

a)168 Seconds
b)178 Seconds
c)188 Seconds
d) 198 Seconds

How to solve this question?

Since one-quarter of clock to another quarter of the clock is 90°, the time of 10 to 12 is sorted. Remaining is 8 to 9 and 12 to 2.
8 to 9=> one third of angle covered by quarter(90÷3)= 30.
12 to 2 => since one third is 30°, two thirds will be 30*2= 60°.
Total angle =90 + 30 + 60 = 180°.

Simple method :

Total hours between 8 am to 2pm (H) = 6 hours (normal counting)
minutes (M)=0.

Use this formula {angle= [30*H - (11/2)*M] }.

Where H= hours, M= minutes. Put the values
Angle = 30*6 - (11/2)*0.
= 180-0 = 180 degrees.

P.S. If minutes are given put that value in same formula.

Min hand take 60 min for complete 360 degree.

So 1 min = 360/60.
1 min = 6 degree.

Hour hand take 12 hours to complete 360 degree.

So 1 min = 360/ (60*12).
1 min = 0.5 degree.

So 8'o clk - 2'o clk = 6 hrs,

1 hour = 0.5*60 = 30 degree.
So 6 hour = 6*30 = 180 degree.

No Rishi. this solution is not good for all problems.
because just think when we have to find angle between 1'o clock and 3'o clock which angle you will consider?
1-3 or 3-1 ?
if 1 to 3 the angle is 60 degrees
if 3 to 1 the angle is 300 degrees

Am I right?

5min = 30dg (degree).

1min = 6dg.

If min 6 dg = hr 1/2 dg.

So angle between hr and min hand is 6*30 = 180dg.

Now from 12, hr hand is shifted and we have to call that shift.

So from 12, min hand is 25 min.

So 25*1/2 = 17.5dg.

Now 180+17.5dg = 197.5dg.

@Rupa.

If the first time is 1'o'clock a second time is 3'o'clock then definitely you will take between 1 & 3 = 60°.

On the other hand, if it is mentioned as first time 3 and the second time 1 then you will take between 3 & 1 = 300°.

AS the question say time is 8am-2pm.
Time between 8am-2pm is 6 hours gap.

Now, we have 12 hours. Which is 12=360deg.(the clock rotates).
After that we take 6 hours and total degree(360)of 12 hours.

Which looks like this:
360/12*6=180deg.