How many times in a day, are the hands of a clock in straight line but opposite in direction?
Answer: B
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.
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Through how many degrees does the hour hand of a clock move in 3 hours and 20 minutes ?
Answer: B
Correct answer: 100°
The hour hand covers \(360°\) in 12 hours, so it moves \(30°\) per hour, or \(0.5°\) per minute.
\[3 \times 30 + 20 \times 0.5 = 90 + 10 = 100°\]
The minute hand, by contrast, would sweep \(1200°\) in the same interval.
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The angle between the minute hand and the hour hand of a clock when the time is 8.30, is
Answer: B
At 8 o’ clock, the hour hand is at 240 degrees from the vertical.
In 30 minutes,
Hour hand = 240 + 30 x (0.5) = 240 + 15 = 255 (The hour hand moves at 0.5 dpm)
Minute hand = 30 x (6) = 180 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 255 - 180 = 75 degrees
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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: B
The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is
\[ \theta = \left| 30H - 5.5M \right| \]
\[ \left| 240 - 5.5M \right| = 180 \]
\[ 5.5M = 60 \quad\Longrightarrow\quad M = \frac{120}{11} \]
That is \( 10\tfrac{10}{11} \) minutes past 8. The other root, \( 5.5M = 420 \), gives \( M = 76.4 \), beyond the hour.
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At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
Answer: D
The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is
\[ \theta = \left| 30H - 5.5M \right| \]
Opposite directions means \( \theta = 180 \), with \( H = 4 \):
\[ \left| 120 - 5.5M \right| = 180 \]
\[ 5.5M = 300 \quad\Longrightarrow\quad M = \frac{600}{11} = 54\tfrac{6}{11} \]
The other root, \( 5.5M = -60 \), is negative and discarded.
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In 6 minutes, how many degrees minute hand traverses?
Answer: D
The minute hand covers \( 360^{\circ} \) in sixty minutes:
\[ \frac{360}{60} = 6^{\circ} \text{ per minute} \]
\[ 6 \times 6 = 36^{\circ} \]
The 6° option is the rate rather than the total, and 30° is the hour hand's hourly figure.
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How many times are the hands of a clock at right angle in a day?
Answer: C
In each twelve-hour period the hands are at right angles 22 times - twice in most hours, but the crossings near 3 and 9 o'clock overlap so that two are lost.
\[ 22 \times 2 = 44 \text{ times in 24 hours} \]
The count is not 48, because between 2–3 and 3–4 (and again around 9) one right angle is shared rather than occurring twice.
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My watch, which gains uniformly, is 2 min and show at noon on Sunday, and is 4 min 48 seconds fast at 2PM on the following Sunday when was it correct?
Answer: D
At noon on Sunday watch gains 2 Minutes.
And at 2PM on following Sunday it is 4 Minutes 48 Seconds fast.
So, it gains 6 Minutes 48 Seconds i.e. 2 Minutes + 4 Minutes 48 Seconds (total 408 Seconds) in 170 Hours (Hours from Sunday Noon (12PM) to following Sunday 2PM)
Therefore, watch gains 120 Seconds (2 Minutes) in 170*120/408 = 50 Hours
50 Hours = 2 Days 2 Hours
Thus, Watch was correct after 2 days 2 hours from Sunday noon that is Tuesday 2PM.
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A clock gains 10 minutes in 24 hours. It is set right at 8 a.m. on Monday. What will it show at 8 a.m. on the following Monday ?
Answer: D
Correct answer: 9:10 a.m.
From one Monday to the next is exactly 7 days.
\[\text{Total gain} = 7 \times 10 = 70 \text{ minutes} = 1 \text{ hour } 10 \text{ minutes}\]
Running ahead by that amount, the clock shows 9:10 a.m. when the true time is 8 a.m.
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An accurate clock is started at noon. By 10 minutes past 3, the hour hand has turned through:
Answer: B
The hour hand turns \( 30^{\circ} \) an hour, or \( 0.5^{\circ} \) a minute.
From noon to 3:10 is \( 3\tfrac{1}{6} \) hours:
\[ 3\tfrac{1}{6} \times 30 = 95^{\circ} \]
The extra ten minutes contribute \( 10 \times 0.5 = 5^{\circ} \), which is what lifts the answer above the whole-hour figure.
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