At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
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Solution:-
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
=> To be coincident, it must gain 15 min. spaces
As 55 min. are gained in 60 min.
=> 15 min. are gained in = (60/55 * 15) = 16 4/11
Hence,the hands are coincident at 16 4/11th minute past 3.
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
=> To be coincident, it must gain 15 min. spaces
As 55 min. are gained in 60 min.
=> 15 min. are gained in = (60/55 * 15) = 16 4/11
Hence,the hands are coincident at 16 4/11th minute past 3.
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