CLOCK CLOCK © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK CLOCK Introduction:- The shape of a clock is generally circular shaped & is divided in to 12 equal parts. According to angle wise the circle consists of 360 degree. So angle wise a clock is 360 degree & each part is 30 degree. The circumference of a clock is divided in to 60 equal spaces so each part is 5 minute spaces. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK CLOCK In one hour, when the minute hand of clock moves around the whole circumference which is 60 minute spaces, the hour hand moves 5 minute spaces. As they move in the same direction, the minute hand gains 55 minute spaces over the hour hand in 60 minutes. So that, the minute hand gains 11 minute spaces in 12 minutes. So from the above one , the minute hand gains 1 minute space over the hour hand in 1+1/11 minutes. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK SOME IMPORTANT POINTS: (i) In 1 minute when the minute hand moves 6 degrees, the hour hand moves 1/2 degree. (As 360 degree of the circle is divided in to 60 minutes.) Thus, in 1 minute the minute hand gains 5+1/2 degrees. (ii) In every hour, both the hands coincide once. In 12 hour they coincide 11 times & in a day 22 times since there is a common position at 12 o'clock. (iii) The hands of a clock are at right angles twice in every hour, but in 12 hours they are at right angles 22 times & in a day 44 times since there are two common positions in every 12 hours. In these positions the hands are 15 minute spaces apart. (iv The hands of a clock are opposite in directions once in every hour& in these position, the hands are 30 minutes apart. (v) If both the hands start moving together from the same position, both the hands will coincide after 65+5/11 minutes. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Too Fast And Too Slow: If a watch indicates 9.20, when the correct time is 9.10, it is said to be 10 minutes too fast. And if it indicates 9.00, when the correct time is 9.10, it is said to be 10 minutes too slow. © vidyog consultants pvt. ltd., bbsr , 2006 EXAMPLE: CLOCK At what time between 4 and 5 o’clock are the hands of the clock together? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution: At 4 o’clock, the hour hand is at 4 and the minute hand is at 12. It means that they are 20 min spaces apart. To be together, the minute hand must gain 20 minutes over the hour hand. Now, we know that 55 min. are gained in 60 min. Therefore, 20 min are gained in (60/55)*20 =240/11 =21(9/11) min. Therefore, the hands will be together at 21(9/11) min past 4. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Question - 1 At what time between 3 & 4 o'clock will the hands of a clock are 5 minutes apart? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution: At 3 o'clock, the hands are 15 minutes apart. In this case there are two cases to be 5 minutes apart. Case: I when the minute hand is 5 minutes behind the hour hand. In this case, the minute hand has to gain 10 minutes spaces in 10+10/11 minutes. So the time is 10 (10/11) minutes past 3 o’clock. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Case ii: When the minute hand is 5 minutes ahead of the hour hand. In this case the minute hand has to gain 15+5 i.e.20 minutes in 20+20/11 minutes i.e.21 9/11 minutes. So the time is 21 9/11 minutes past 3 o’clock. © vidyog consultants pvt. ltd., bbsr , 2006 Question - 2 CLOCK At what time between 4 & 5 o’clock will the hands of a clock are at right angle? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution: At 4 o’clock both the hands are 20 minutes apart. When they are at right angle they are 15minutes apart & this is possible in two cases. Case i: When the minute hand is 15 minutes behind the hour hand. In this case the minute hand has to gain 5 minutes spaces which are possible in 5+5/11 minutes. So the time is 5 5/11minutes past 4 o’clock. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Case ii: When the minute hand is 15 minutes ahead of the hour hand. In this case the minute hand has to gain 20+15 =35 minutes spaces in 35+35/11 minutes. So the time is 38(2/11) minutes past 4 o'clock © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Question - 3 At what time between 4 & 5 o’clock will the hands of a clock are in opposite direction? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution:At 4 o’clock both the hands are 20 minutes apart .But when they are opposite in direction they are 30 minutes apart. In this case the minute hand has to gain 20+30=50 minutes spaces. (As hands can not move in anti clock wise) So the minute hand can gain these 50 minutes in 50+50/11 minutes. There fore at 54 6/11minutes past 4 o’clock they are in opposite in direction. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Question - 4 A watch, which gains uniformly, is 2 minutes slow at noon on Sunday, and is 4 minutes 48 seconds fast at 2 p.m. on the following Sunday. When was it correct? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution:According to the question, the watch gains 2minutes+4 minutes 48 seconds i.e.6 4/5 minutes or 34/5 minutes in170 hour. (As the duration of the time from 12 noon on Sunday to2 p.m. on the following Sunday is 170 hours) The watch was correct when it gains the slow time of 2 minutes. So the watch gains these 2 minutes slow in 2*5/34*170 i.e. in 50 hours. These 50 hours =2 days& 2 hours. So the watch was correct after 2 days 2 hours from Sunday noon, i.e. at 2 p.m. on Tuesday. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Question - 5 A watch, which gains 5 seconds every 3 minutes, is set right at 6 a.m. What is the true time in the afternoon of the same day when the watch indicates a quarter past 3? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution:According to the wrong clock, when the time is 3 minutes 5 seconds it is 3 minutes on the correct clock. The wrong clock, in 3 minutes 5 seconds gains 5seconds. So in 9 hours 15 minutes, it gains 15 minutes. (As from 6 a.m. to quarter past 3, the duration is 9 hours 15 minutes) Hence the true time is 15 minutes behind 15 minutes past 3 i.e. 3 p.m. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Question - 6 How much time does a clock gain or loses per day if its hands coincide every 66 minutes? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution:In correct clock both hands coincide at an interval of 65 5/11 minutes. So in this case, in 66 minutes the clock loses 6/11 minutes... In 1 hour or 60 minutes the clock lose ( 6/11)*(1/66)*60 minutes. So in a day in 24 hours the clock lose 6/11*1/66*60*24=1440/121 minutes. © vidyog consultants pvt. ltd., bbsr , 2006 Question - 7 CLOCK A clock loses 5 seconds an hour and is set right Sunday at noon. What time will it indicate on the following Monday at noon? © vidyog consultants pvt. ltd., bbsr , 2006 Database structure CLOCK Solution:According to this wrong clock when the time is 59 minutes 55 seconds, it is 60 minutes in correct clock. The wrong clock, in 59 minutes 55 seconds loses 5 seconds. So in24 hours, it loses 120 seconds or 2 minutes. © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Question - 8 A clock is set right at 8 am. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 pm on the following day? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution:Time from 8 am on a day to 1 pm on the following day is 29 hrs. Now, 24 hrs 10 min of this clock are the same as 24 hrs of the correct clock. i.e.145/6 hrs of this clock = 24 hrs of correct clock. 29 hrs of this clock = (24*6/145)*29 hrs of correct clock. = 28 hrs 48 min of correct clock. So, the correct time is 28 hrs 48 min after 8 am or 48 min past 12. © vidyog consultants pvt. ltd., bbsr , 2006 Question - 9 CLOCK A clock is set right at 4 a.m. The clock loses 20 min in 24 hours. What will be the true time when the clock indicates 3 a.m. on 4th day? © vidyog consultants pvt. ltd., bbsr , 2006 CLOCK Solution:Time from 4 am to 3 am on 3rd day = 24*3-1 = 71 hrs. Now, 23(2/3)=71/3 hrs 40 min of this clock = 24 hrs of correct clock. or, hrs of this clock = 24 hrs of the correct clock. Therefore, 71 hrs of this clock = 24*3*71/71=72 hrs of correct clock. So, the correct time = 3 am + (72-71) = 4 am. © vidyog consultants pvt. ltd., bbsr , 2006

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# minutes past 4 o`clock