Ques: At what time between 2 and 3 pm, minute hand and hour hand of clock are together?

      a) 2/11 hrs past 2 pm.          B) 2/9 hrs past 2 pm.     C) 2:10 pm     

      d) None.

Soln: Recall what we taught in CLOCKS class. Speed of MH is 6 degree per minute and that of HH is ½ degree per minute. And hence relative speed of MH over HH is 5.5 degree per minute.

Also recall, we cleared that on the dial of a clock there are 60 minute spaces.

Minute spaces are different from Minutes. Minute spaces are unit of distance while minute is unit of time. Also note MH will travel 1 minute space in 1 minute while HH will travel 1 minute space in 12 minutes. Why so? Refer back your class notes.

Let me explain again. 60 minute spaces on the face of clock mean an angle of 360 degree. Hence 1 minute space means an angle of 6 degree. Now it being 6 degree, MH will cover it in 1 minute(MH’s speed being 6 degree per minute) while HH will cover in 12 minutes(HH’s speed being ½ degree per minute).

Now let’s use this concept to answer the ques above.

At 2 pm, situation is MH is at 12 and HH is at 2. That means that MH is 10 minute spaces or 60 degree behind HH. So MH and HH will coincide when MH will cover 60 degree over HH. MH will cover(Mind it cover and not travel, those who could not get it please refer to Time Speed Distance Relative Speed notes) 60 degree @ 5.5 degree per minute. And in order to do so it will take

60 / 5.5 minutes = 120 by 11 minutes = 10 minutes and 10/11 minutes.

Lets convert 10/11 minutes into seconds.

10/11 * 60 seconds = 600/11 seconds = 54 seconds nearly.

Hey guys, we can also go into fractions of seconds if we want. But is that required.

Now, in this particular question, options have been given in hrs and not minutes. So in this case when we got 60 / 5.5 minutes, we will convert that into hrs and not minutes. And that will be

60/5.5 minutes = 60 / (5.5 x 60 ) hrs = 1 / 5.5 hrs = 2 / 11 hrs. Hence the option A.

I explained the entire concept for the benefit of those who are new to this chapter CLOCKS. Guys note that CLOCKS is no different from T,S and D and Relative speed concept.

Regards

TVM