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1.	The reflex angle between the hands of a clock at 10.25 is:
Answer» Angle traced by hour hand in 125 hrs = 360 x 125 ° = 312 1 ° . 12 12 12 2 Angle traced by minute hand in 25 min = 360 x 25 ° = 150°. 60 Reflex angle = 360° - 312 1 - 150 ° = 360° - 162 1 ° = 197 1° . 2 2 2

2.	At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
Answer» At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30 min. spaces apart. Minute hand will have to gain 50 min. spaces. 55 min. spaces are gained in 60 min. 50 min. spaces are gained in 60 x 50 min. or 54 6 min. 55 11 Required time = 54 6 min. past 4. 11

3.	How many times in a day, are the hands of a clock in straight line but opposite in direction?
Answer» 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 o'clcok only). So, in a day, the hands point in the opposite directions 22 times.

4.	A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
Answer» Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = 37 hrs. 4 3 min. 5 sec. of this clock = 3 min. of the correct clock. 37 hrs of this clock = 1 hrs of the correct clock. 720 20 37 hrs of this clock = 1 x 720 x 37 hrs of the correct clock. 4 20 37 4 = 9 hrs of the correct clock. The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.

5.	How much does a watch lose per day, if its hands coincide every 64 minutes?
Answer» 55 min. spaces are covered in 60 min. 60 min. spaces are covered in 60 x 60 min. = 65 5 min. 55 11 Loss in 64 min. = 65 5 - 64 = 16 min. 11 11 Loss in 24 hrs = 16 x 1 x 24 x 60 min. = 32 8 min. 11 64 11

6.	At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
Answer» When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 60 x 5 min = 5 5 min. 55 11 Required time = 5 5 min. past 7. 11

7.	The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Answer» Angle traced by hour hand in 13 hrs = 360 x 13 ° = 130°. 3 12 3 Angle traced by min. hand in 20 min. = 360 x 20 ° = 120°. 60 Required angle = (130 - 120)° = 10°.

8.	At what angle the hands of a clock are inclined at 15 minutes past 5?
Answer» Angle traced by hour hand in 21 hrs = 360 x 21 ° = 157 1 ° 4 12 4 2 Angle traced by min. hand in 15 min. = 360 x 15 ° = 90°. 60 Required angle = 157 1 ° - 90° = 67 1 ° 2 2

9.	At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
Answer» At 3 o'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 60 x 15 min = 16 4 min. 55 11 The hands are coincident at 16 4 min. past 3. 11

10.	How many times do the hands of a clock coincide in a day?
Answer» The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). AM 12:001:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 PM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 The hands overlap about every 65 minutes, not every 60 minutes. The hands coincide 22 times in a day.

11.	How many times in a day, the hands of a clock are straight?
Answer» In 12 hours, the hands coincide or are in opposite direction 22 times. In 24 hours, the hands coincide or are in opposite direction 44 times a day.

12.	How many times are the hands of a clock at right angle in a day?
Answer» In 12 hours, they are at right angles 22 times. In 24 hours, they are at right angles 44 times.

13.	The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
Answer» Angle traced by hour hand in 17 hrs = 360 x 17 ° = 255°. 2 12 2 Angle traced by min. hand in 30 min. = 360 x 30 ° = 180°. 60 Required angle = (255 - 180)° = 75°.

14.	At what time between 9 and 10 o'clock will the hands of a watch be together?
Answer» To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces. 55 min. spaces gained in 60 min. 45 min. spaces are gained in 60 x 45 min or 49 1 min. 55 11 The hands are together at 49 1 min. past 9. 11

15.	At 3:40, the hour hand and the minute hand of a clock form an angle of:
Answer» Angle traced by hour hand in 12 hrs. = 360°. Angle traced by it in 11 hrs = 360 x 11 ° = 110°. 3 12 3 Angle traced by minute hand in 60 min. = 360°. Angle traced by it in 40 min. = 360 x 40 ° = 240°. 60 Required angle (240 - 110)° = 130°.

16.	At what time between 5.30 and 6 will the hands of a clock be at right angles?
Answer» 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 60 x 40 min = 43 7 min. 55 11 Required time = 43 7 min. past 5. 11

17.	A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
Answer» Angle traced by hour hand in 12 hrs = 360°. Angle traced by hour hand in 5 hrs 10 min. i.e., 31 hrs = 360 x 31 ° = 155°. 6 12 6