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navnath

· started a discussion

· 1 Months ago

1 (Question: 186014.0 )

give explination

Question:
At what time between 3 and 4 O'clock will the minute hand be 4 minutes behind the hour hand ?
Options:
A) 3 hours 14 minutes
B) 3 hours 16 minutes
C) 3 hours 12 minutes
D) Cannot be determined
Solution:
Ans: (c)


second method:


At 3:00 , the minute hand is 15 min. spaces apart from the hour hand.


To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

15 min. are gained in 60/55x15 minutes= 16 and 4/11 minutes

The hands are coincident at 16 and 4/11 minutes past 3

At 3 hours and 16 and 4/11 = 16 - 4 = 12 minutes between 3 and 4 will the minute hand be 4 minutes behind the hour hand.

Alternate solution: 

    According to question, We know the approximate time is 3 hour 11 minute

    but we can find out the exact value =  minute hand \(\times\) 60/55

                                                        = 3 : (11 x 60/55)

                                                         = 3 : 12 min


Akhil George

· commented

· 1 Months ago

As the minute hand covers 60 minutes or 60 markings on the clock, the hour hand covers 5 markings. so 1 marking of hour hand will be 60/5 = 12 minutes/marking of minute hand. As the clock reaches 3 hours 12 minutes, the hour needle will be pointing on the 16th minute/marking. That gives a difference of 4 minutes.

Knowledge Expert

· commented

· 1 Months ago

When minute hand covers 60 minutes that is passed by hour hand only 5 minutes space which alternatively we can say 1 hour for hour hand. But here among space covered by minute hand i.e. 60 minutes. Hour hand expenses only 5 minute equals i.e. 1 hour. So gained by minute hand is 55 minutes.
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