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Question 1: At what time between 5 to 6 O’clock will the hands of a clock point coincide with each other? Solution: As you know, the angle between the hour hand and minutes hand is 0. H = 5 and angle is 0 degree 0 = 30 x 5 – 11 M/2 150 = 11 M/2 300 = 11M M = 27(3/11) Minutes Therefore, the correct response for this question is 27(3/11) Minutes past to 7. Question 2: What will be the angle between the hour and minute hands of the clock at 7:30? Solution: Angle at 7:30 is: I60H – (11M / 2) = θI (60 x 7 – 11 x 30) / 2 = θ 420 – 330 / 2 = θ θ = 90 / 2 = 45 degree Question 3: If it is 5:40 in the 12 hours clock then what will be the time in the mirror? Solution: For every mirror image based on a clock if it is a 12 hours clock, then candidates need to subtract the given timing from 11:60 hours, whereas if it is a 24 hours clock then candidates need to subtract the given time from 23:60 hours. Hence, we get 11:60 – 5:40 = 6:20 as it is a 12 hours clock. Question 4: If the water image of the clock shows 3 hours 25 minutes, then what will be the actual time? Solution: For every water image based on the clock reasoning section if the minute is less than 30 then candidates need to subtract the given time from 18:30 hours, whereas if it is more than 30 then candidates need to subtract the given time from 18:90 hours. Hence, 18:30 – 3:25 = 15:03 or 3 hours 5 minute (as the minutes are less than 30) Question 5: The clock was set on Thursday, at 4 AM. If the clock gains 20 minute per hour, then what will be the time that the clock shows on Friday, 8:30 PM? Solution: The clock was set on Thursday, at 4 AM. So if we calculate the time from Thursday, 4 AM to Friday, 8:30 PM then it will be 40 hours 30 minutes. As mentioned in the question, the clock gains 20 minutes per hour. So, the clock will get 810 minutes in 40 hours 30 minutes. Hence, the clock will show the time 8:30 PM + 810 minutes = 10 AM of Saturday on Friday, 8: 30 PM. Question 6: A watch gains 4 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day? Solution: The watch gains 5 seconds in 3 minutes so it will be 100 seconds in 1 hour. From 8 AM to 10 PM on the same day, the total time passed is 14 hours. Hence, in 14 hours the clock would have gained 1400 seconds or 23 minutes 20 seconds. So, when the correct time is 10 PM, the watch would show 10 hours 23 minutes 20 seconds per minute.

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A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 15 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)? A. 5:00 B. 5:34 C. 5:42 D. 6:00 E. 6:24

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