


1.
Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.
Answer & Solution
Answer: d) 47 1/2 degree
Solution: Angle traced by the hour hand in 12 hours = 360 degree Angle traced by it in 3 hrs 25 min, (i.e) 41/12 hrs = [(360/12) * (41/12)] degree = 102 1/2 Angle traced by minute hand in 60 min. = 360 degree Angle traced by it in 25 min. = [(360/60) * 25] degree = 150 degree Required angle = [150 degree  102 1/2] = 47 1/2 degree 2.
At what time between 2 and 3'o clock will the hands of a clock be together?
Answer & Solution
Answer: c) 10 (10/11) min. past 2
Solution: At 2'0 clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min. spaces apart. To be together, the minute hand must gain 10 minutes over the hour hand. Now, 55 minutes are gained by it in 60 min. 10 minutes will be gained in [(60/55) * 10] min. = 10 (10/11) min. The hands will coincide at 10 (10/11) min. past 2. 3.
At what time between 4 and 5 'o clock will the hands of a clock be at right angle?
Answer & Solution
Answer: b) 5 5/11 min. past 4, 38 2/11 min. past 4
Solution: At 4'o clock, the minute hand will be 20 min. spaces behind the hour hand. Now, when the two hands are at right angles, they are 15 min. spaces apart. So, they are at right angles in following two cases. Case I : When minute hand is 15 min. spaces behind the hour hand: In this case, minute hand will have to gain (20  15) = 5 minute spaces. 55 min. spaces are gained by it in 60 min. 5 min. spaces will be gained by it in [(60/55) * 5] min. = 5 5/11 min. They are at right angles at 5 5/11 min. past 4. Case II: When the minute hand is 15 min. spaces ahead of the hour hand : To be in this position, the minute hand will have to gain (20 + 15) = 35 minutes spaces. 55 min. spaces are gained in 60 min. 35 min. spaces are gained in [(60/55) * 35] min. = 38 2/11 min. They are at right angles at 38 2/11 min. past 4. 4.
Find at what time between 8 and 9'o clock will the hands of a clock be in the same straight line but not together.
Answer & Solution
Answer: d) 10 10/11 min. past 8
Solution: At 8'o clock , the hour hand is at 8 and the minute hand is at 12, (i.e) the two hands are 20 min. spaces apart. To be in the same straight line between but not together they will be 30 minute spaces apart. So, the minute hand will have to gain (30  20) = 10 minute spaces over the hour hand. 55 minute spaces are gained in 60 min. 10 minute spaces will be gained in [(60/55) * 10] min. = 10 10/11 min. The hands will be in the same straight line but not together at 10 10/11 min. past 8. 5.
At what time between 5 and 6'o clock are the hands of a clock 3 minutes apart?
Answer & Solution
Answer: b) 24 min. past 5, 31 5/11 min. past 5
Solution: At 5'o clock, the minute hand is 25 min. spaces behind the hour hand. Case I: Minute hand is 3 min. spaces behind the hour hand. In this case, the minute hand has to gain (25  3) = 22 minute spaces. 55 min. are gained in 60 min. 22 min. are gained in [(60/55) * 22] min. = 24 min. Therefore, The hands will be 3 min. apart at 24 min. past 5. Case II: Minute hand is 3 min. spaces ahead of the hour hand. In this case, the minute hand has to gain ( 25 + 3) = 28 minute spaces. 55 min gained in 60 min. 28 min. are gained in [(60/55) * 28] = 31 5/11 min. Therefore, The hands will be 3 min. apart at 31 5/11 min. past 5. 6.
The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose?
Answer & Solution
Answer: c) gains 10 10/43 min in 24 hours
Solution: In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes. To be together again, the minute hand must gain 60 minutes over the hour hand. 55 min. are gained in 60 min. 60 min. are gained in [(60/55) * 60] min. = 65 5/11 min. But, they are together after 65 min. Gain in 65 min. = [(65 5/11)  65] = 5/11 min. Gain in 24 hours = [(5/11) * {(60 * 24) / 65}] min. = 10 10/43 min. The clock gains 10 10/43 min in 24 hours. 7.
A watch which gains uniformly is 5 min. slow at 8'o clock in the morning on Sunday and it is 5 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct?
Answer & Solution
Answer: d) 20 min. past 7 p.m on Wednesday
Solution: Time from 8 a.m. on Sunday to 8 p.m. on following Sunday = 7 day 12 hours = 180 hours The watch gains [5 + 5 4/5] min. or 54/5 min. in 180 hrs. Now, 54/5 min. are gained in 180 hrs. 5 min are gained in [180 * (54/5) * 5] hrs = 83 hrs 20 min. = 3 days 11 hrs 20 min. Watch is correct 3 days 11 hrs 20 min. after 8 a.m. of Sunday. Therefore, It will be correct at 20 min. past 7 p.m on Wednesday. 