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Nagalakshmi

· started a discussion

· 1 Months ago

Doubt (Question: 186014.0 )

Please provide short cuts to solve these type of clock problems

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


Knowledge Expert

· commented

· 1 Months ago

Dear student,
1M = 6degree

Used the formula; Angle(thita) = 30H - 11/2M
4*6degree = 30 *3 - 11/2*M
24 = 90 - 11/2 * M
M = 12min.
Ans. 3 hour 12 min.


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