Clocks and Calendar - Clock Problem


 
 
Concept Explanation
 

Clocks and Calendar - Clock Problem

Clocks and Calendar - Clock Problem: This concept revolves around the calculation of the angular distance traversed by the different hand of the clock. The different hands of the clock move with different speed.The hour hand takes 12 hours to traverse an angle of 360 degree, and the minute hand completes one rotation in one hour i.e. it covers 360^{0} in 1 hour .

Speed of minute hand = 360^{0} in 1 hour ( 60 min )

                                    = 6^{0} per minute

Speed of hour hand = 360^{0} in 12 hours

                              = 30^{0} in 1 hour ( 60 min )

                             = left ( frac{1}{2} right )^0; per;minute

As they are moving in the same direction

So, the relative speed of minute hand over hour hand will be difference of their speeds

 =6^{0}-frac{1^{0}}{2}=frac{11^{0}}{2}; per; minute

Illustration:  At what time immediately after 2 o' clock, do the hands of clocks coincide?

A. 10 minutes 11 seconds.            B. 10 minutes 10 seconds.    C. 10 minutes 55 seconds.         D.  9 minutes 55 seconds.

Answer: C

Solution: At 2 o'clock, the hands of the clock are 60^{0} apart.

The minute hand covers this 60^{0} at a speed of frac{11^{0}}{2} per minute.

To cover frac{11^{0}}{2}, time required = 1 min

TO cover 60^{0} , time required =frac{2}{11}times60^{0}

                                              =frac{120}{11}

                                              =10frac{10}{11} minutes

If we convert frac{10}{11} minutes to seconds, it is equal to frac{10}{11}times60

                                               = 55 seconds (approx)

So, the answer is 10 minutes 55 seconds.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A clock is set right at 10 am. the clock gains 10 minute in 24 hours. What will be the right time when the clock indicates 1 pm on the following day?

Right Option : B
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Explanation
Question : 2

At what time immediately after 3 o' clock, do the hands of clocks coincide?

Right Option : D
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Explanation
Question : 3

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

Right Option : D
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Explanation
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