Clock and Calendar

Q 1. A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day? A)10 p.m B)1 a.m C)12 a.m D)11 p.m Answer : Option D Explanation: Time from 5 am. on a day to 10 pm. on 4th day = 89 hours. Now 23 hrs 44 min. of this clock = 24 hours of correct clock. 356/15 hrs of this clock = 24 hours of correct clock 89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock. = 90 hrs of correct clock. So, the correct time is 11 p.m. Q 2. How much does a watch lose per day, if its hands coincide ever 64 minutes? A)32 8/11 B)36 8/11 C)34 8/11 D)33 8/11 Answer : Option A Explanation: 55min spaces are covered in 60min 60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min. loss in 64min=(65+5/11)- 64 =16/11 Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11. Q 3. Find the angle between the hour hand and the minute hand of a clock when the time is 3.25Find the angle between the hour hand and the minute hand of a clock when the time is 3.25 A)55.5 degrees B)49.5 degrees C)52.5 degrees D)47.5 degrees Answer : Option D Explanation: At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins. Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5° Hence, Angle between Hour and the Minute hand = ( 60 - 12.5 ) = 47.5° Q 4. At what time between 5.30 and 6 will the hands of a clock be at right angles? A)5 min B)(43 + 5/11) min past 5 C)(43 + 7/11) min pats 5 D)12 min Answer : Option C Explanation: At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min 40 min. spaces are gained in min in 60/55*40 min

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