In 12 hours both hands are in straight line (either coincides or in opposite direction) 22 times. Hence in 24 hours both hands are in straight line 44 times.
22
The minute hand to coincide with the hour hand it should trace at first 5 minute spaces and then the hands of the clocks to be opposite to each other minute hand should trace 30 minute spaces i.e. totally it should gain 5 + 30 = 35 minute spaces to be opposite to that of hour hand.
We know that, Minute hand gains 55 minute spaces over hour hand in 1 hour. Therefore, Minute hand gain 40 minute spaces over hand in 35 x (60/55) = 38(2/11).
Hence the hand of the clock will minutes be opposite to each at 38 (2/11) past 1'O clock. Therefore, Correct option is B.
28 x 2 x 6 = 336 degree
Consider exactly at 8 : 00, minute hand is at position '12' and hour hand is at '8' hence angle between these two hands at 8 : 00 is 240°.
Case (i) when minute hand is behind Hour hand then required time is (240 - 90)/(11/2) = 150/(11/2) = 300/11 = 27 3/11 minute
Case (ii) when minute hand is ahead of four hand then required time is (240 + 90)/(11/2) = 330/(11/2)
= 330 x 2/11 = 60 minute i.e., at 9 : 00 PM
9 :164/11
44
From Sunday noon to the following Sunday at 2 p.m. there are 7 days 2 hours or 170 hours. The watch gains 2 + 44/5 min in 170 hrs. Therefor, the watch gains 2 min in 2 x 170 hrs i.e., 50 hours 64/5. Now 50 hours Sunday noon = 2 p.m on Tuesday.
Time from 10 a.m on a day to 3 a.m on 4th day = 24 x 3 + 17 = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
89 hrs of faulty clock = (24 x 15/356 x 89) hrs = 90 hrs.
So, the correct time is 11 p.m
Time from 12 p.m. on Sunday to 2 p.m. on the following Sunday = 7 days 2 hours.
= 24 x 7 + 2 = 170 hours.
The watch gain = (2 + 4 x 4/5) min = 34/5 minute in 170 hrs.
Since, 34/5 min are gained in 170 hrs.
2 min are gained in (170 x 5/34 x 2) hrs = 50 hours i.e., 2 days 2 hrs. after 12 p.m. on Sunday i.e., it will be correct at 2 p.m. on Tuesday.
When we divide 79 by 7 we will get remainder 2 so we have 2 odd days, so required day must be 2 days back from today (i.e Sunday) and that day should be Friday.
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