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Math Topic - Clock

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  1. PBI 1. 2. PBI INSTITUTE CLOCK The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces. A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called minute hand or long hand. (i). In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand. (ii). In every hour, both the hands coincide once. (iii). The hands are in the same straight line when they are coincident or opposite to each other. (iv). When the two hands are at right angles, they are 15 minute spaces apart. (v). When the hands are in opposite directions, they are 30 minute spaces apart. (vi). Angle traced by hour hand in 12 hrs = 3600 (vii). Angle traced by minute hand in 60 min. = 3600 (viii). If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast. (ix). On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow. 1. At what time between 2 and 3 0'clock will the hands of a clock be together? Solution At 2 0'clock, the hour is at 2 and the minute hand is at 12,i.e. they are 10 min. Spaces apart. To bo together, the minute hand must gain 10 minutes over the hour hand. Now,55 minutes will be gained in 60 min. 10 minutes spaces will be gained in (60/55 x10) min. = min. The hands will coincide at 10x10/11 min.past 2. 2. How much does a watch lose per day, if its hands coincide ever 64 minutes? A. min C. 90 min Solution B. min D. 96 min 55 min. spaces are covered in 60 min. 60 min. spaces are covered = 65
  2. PBI PBI INSTITUTE At 8 0'clock, the hour is at 8 and the minute hand is at 12,i.e. the two hands are 20 min. Spaces apart. So, the minute hand gain 55 minutes will be gained in 60 min. = (30 - 20)minute 10 minutes spaces will be gained in (60/55 x10) min. = min. The hands will be in the same straight line but not together at 10x10/11 min.past 8. 4. The angle between the minute hand and the hour hand of a clock when the time is 4.20, A. 00 c. 100 Solution Angle traced by hour hand in13/3 hrs Angle traced by min. hand in 20 min Required angle B. 50 D. 200 = (360/12 x 13/3)0 = 1300 = 1200 = (130 - 120)0 5. At 3.40, the hour hand and the minute hand of a clock form an angle of A. 1200 c. 1300 Solution Angle traced by hour hand in 12 hrs. Angle traced by it in 11/3 hrs. Angle traced by minute hand in 60 min. Angle traced by it in 40 min. Therefore ,Required angle(240-110)0 B. 1250 D. 1350 = 3600 = 3600 = 1300 6. The angle between the minute hand and the hour hand of a clock when the time is 8.30, is A. 800 c. 600 Solution Angle traced by hour hand in 17/2 hrs Angle traced by min hand in 30 min Required angle B. 750 D. 1050 = 255. = 180. = (255 - 180)0 = 750 7. At what angle the hands of a clock are inclined at 15 minutes past 5? A. 58 1/20 c. 67 1/20 B. 640 D. 72 1/20
  3. PBI Solution Angle traced by hour hand in 21/4 hrs. Angle traced by min.hand in 15 min Therefore, the Required angle PBI INSTITUTE = 1571/20 = 900 = [(1571/20)-900] = 671/20 8. How many times are the hands of a clock at right angle in a day? A. 22 C. 44 Solution B. 24 D. 48 In 12 hours, they are at right angles 22 times. Therefore, In 24 hours, they are at right angles 44 times. 9. A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct? A. 2 p.m. on Tuesday C. 3 p.m. on Thursday Solution Time from 12 p.m. on Monday to 2 p.m. on the following = 7 days 2 hours. Monday The watch gains Now,34/5 min are gained in 170 hrs. 2 min are gained in(170x 5/34 x2)hrs. Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m.on Wednesday. 10. At what time, in minutes, between 3 0'clock and 4 0'clock, both the needles will coincide each B. 2 p.m. on Wednesday D. 1 p.m. on Friday =170 hours. = (2 + 4 x4/5)min = 34/ 5 min.in 170 hrs. other? A. 51/11 0 c. 134/110 Solution B. 124/110 D. 164/110 At 3 0'clock, 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 The hands are coincident at 16x4/11 min past3. = (60/55 x 15)min 11. Find the angle between the hour and the minute hand of a clock when the time is 3.25. A. 47 1/2 c. 551/2 B. 49 1/2 D. 571/2
  4. PBI Solution Angle traced by the hour hand in 12 hours Angle traced by it in 3 hrs 25 min Angle traced by minute hand in 60 min Angle traced by it in 25 min. Required angle PBI INSTITUTE = 3600 = 41/ 12 hrs = (360/ 12 x 41 / 12)0 = 102 1/20 = 3600 = (360/ 60 x 25)0 = 1500 = (150- 102 1/20) = 47 1/20 12. How many times in a day, the hands of a clock are straight? A. 22 B. 24 C. 44 D. 48 Solution In 12 hours, the hands coincide or are in opposite direction 22 times. Therefore, In 24 hours, the hands coincide or are in opposite direction 44 times a day. 13. An accurate clock shows 8 0'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 0'clock in the afternoon? A. 1440 c. 1680 Solution Angle traced by hour hand in 5 hrs 10 min. B. 1500 D. 1800 = (360/12 x = 1800 14. A clock is set 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. 9 p.m C. 11 p.m Solution Time from 5 a.m on a day to 10 p.m.on 4th day Now 23 hrs 44 min. of this clock Therefore 356 / 15 hrs of this clock B. 10 p.m D. 12 p.m 89 hrs of this clock = (24 x 15/356 x 89) hrs = 90 hrs So, the correct time = 89 hours. = 24 hours of correct clock. = 24 hours of correct clock. 11 p.m. 15. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
  5. PBI 1450 1550 Solution Angle traced by hour hand 12 hrs Angle traced by hour hand 5 hrs 10 min PBI INSTITUTE in in 1500 1600 = 3600 = 31 / 6 hrs / 12 x 31 / 6] = 1550 16. The reflex angle between the hands of a clock at 10.25 is A. 1800 c. 1950 Solution Angle traced by hour hand in 125 / 12 hrs. Angle traced by minute hand in 25 min. Reflex angle B. 192 1/20 D. 197 1/20 x 125/12]0 = 3121/20 = [360/60 x 2510 = 1500 = 360 - (3121/2 -150)0 =3600 - 162 1/20 = 1971/20 17. How many times in a day, are the hands of a clock in straight line but opposite in direction? A. 20 B. 22 c. 24 D. 48 Solution The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 0'clcok only). So, in a day, the hands point in the opposite directions 22 times.

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