At what time, in minutes, between 3 o'clock and 3.25 pm, both the needles of the clock will coincide each other?
Answer: D
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. spaces are gained in 60/55 x 15 = 16 4/11 min
The hands are co-incident at 16 (4/11) past 3.
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A clock is set right at 5 am the clock loses 16 min in 24 hours. What will be the right time when the clock indicates on 3 pm the 8th day?
Answer: B
Time from 5 am On a day to 3 pm on 8th day = 178 hours
Now 23 hrs 44 min. of this clock = 24 hours of correct clock
365/15 hrs of this clock = 24 hours of correct clock
178 hrs of this clock = (24 × 15/356 × 89) hrs of correct clock
= 180 hrs of correct clock.
So, the correct time is 5 pm.
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How much does a watch gain or lose per day, if its hands coincide every 64 minutes?
Answer: D
55 min. spaces are covered in 60 min.
60 min. spaces are covered in (60/55 × 60) min = 65 5/11 min
Loss in 64 min = (65 5/11 - 64) = 16/11 min
Loss in 24 hrs= (16/11 × 1/64 × 24 × 60) min = 32 (8/11) min.
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At what time between 7.02 and 8.02 will the hands of a watch be in the straight line but no together?
Answer: B
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 must gain only 5 min. space
55 min. spaces are gained in 60 min.
5 min. spaces are gained in (60/55 × 5) min = 5 (5/11) min.
Required time = 5 (5/11) min. past 7.
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At what time between 3 & 4 will the hands of a watch point in opposite directions?
Answer: C
At 3 o'clock, the hands of the watch are 15 min. space apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand must gain 45 min. space (15 + 30 min)
55 min spaces are gained in 60 min.
45 min. spaces would be gained in (60/55 × 45) min.
Required time = 49 1/11 min. past 3.
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How many times do the hands of a clock coincide in a day?
Answer: B
In twelve hours the hands coincide eleven times, not twelve: between 11 and 12 they meet only at 12 o'clock itself, so that hour contributes no separate coincidence.
\[ 11 \times 2 = 22 \text{ times in 24 hours} \]
Equivalently, the minute hand laps the hour hand once every \( \tfrac{720}{11} = 65\tfrac{5}{11} \) minutes, and \( \tfrac{1440}{720/11} = 22 \).
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When the time in the clock is 7.20 pm, then the angle between the hands of the clock is
Answer: C
At 7 o’ clock, the hour hand is at 210 degrees from the vertical.
In 20 minutes,
Hour hand = 210 + 20 x (0.5) = 220 (The hour hand moves at 0.5 dpm)
Minute hand = 20 x (6) = 120 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 220 - 120 = 100 degree
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At what time between 5.30 & 6 will the hands of a watch be at right angle?
Answer: A
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 must gain 40 min
55 min. spaces are gained in 60 min.
40 min. spaces would be gained in (60/55 × 40) min. = 43 7/11 min.
Required time = 43(7/11) min. past 5.
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At what time between 9.13 and 10.12 will the hands of a watch be together?
Answer: B
To be together between 9 and 10 o'clock, the minute hand must gain 45 min. space
55 min. spaces are gained in 60 min.
45 min spaces would be gained in (60/55 × 45) min. or 49 1/11 min.
The hands are together at 49 1/11 min. past 9.
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At what angle the hands of a clock are inclined at 40 minutes past 2?
Answer: B
At 2 o’ clock, the hour hand is at 60° from the vertical.
In 40 minutes,
Hour hand = 60 + 40 x (0.5) = 80° (The hour hand moves at 0.5 dpm)
Minute hand = 40 x (6) = 240° (The minute hand moves at 6 dpm)
Difference or angle between the hands = 240 - 80 = 160°
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