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Q:

At what time between 2 and 3 o'clock will the hands of a clock be together?

A) (9 + 10/11) min past 2	B) (10 + 10/11) min past 2
C) (11 + 10/11) min past 2	D) (12 + 10/11) min past 2

Answer & Explanation Answer: B) (10 + 10/11) min past 2

Explanation:

At 2 o'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.

$\therefore$ 10 minutes will be gained in $\frac{60}{55} \times 10$ min. = $10 \frac{10}{11}$ min.

The hands will coincide at $10 \frac{10}{11}$ min. past 2.

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Q:

Find the angle between the hour hand and the minute hand of a clock when the time is 3.25

A) 47.5 degrees	B) 57.5 degrees
C) 45.5 degrees	D) 55.5 degrees

Answer & Explanation Answer: A) 47.5 degrees

Explanation:

At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.

Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°

Hence, Angle between Hour and the Minute hand = ( 60 - 12.5 ) = 47.5°

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Q:

How many times do the hands of a clock coincide in a day?

A) 20	B) 21
C) 22	D) 23

Answer & Explanation Answer: C) 22

Explanation:

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).

The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.

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Q:

At what time between 9 and 10 o'clock will the hands of a watch be together?

A) (49 + 3/11) min past 11	B) (49 +1/11) min past 9
C) (45 +1/11) min past 9	D) (45 +7/11) min past 11

Answer & Explanation Answer: B) (49 +1/11) min past 9

Explanation:

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 $\frac{60}{55} \times 45$ min or $49 \frac{1}{11}$ min

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Q:

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

A) 54 past 4	B) (53 + 7/11) past 4
C) (54 + 8/11) past 4	D) (54 + 6/11) past 4

Answer & Explanation Answer: D) (54 + 6/11) past 4

Explanation:

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 $\frac{60}{55} \times 50$ min. or $54 \frac{6}{11}$

Required time = $54 \frac{6}{11}$ min. past 4.

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Q:

How many times in a day, are the hands of a clock in straight line but opposite in direction?

A) 11	B) 22
C) 33	D) 44

Answer & Explanation Answer: B) 22

Explanation:

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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Q:

How many times are the hands of a clock at right angle in a day?

A) 44	B) 54
C) 64	D) 22

Answer & Explanation Answer: A) 44

Explanation:

In 12 hours, they are at right angles 22 times.
$\therefore$ In 24 hours, they are at right angles 44 times.

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Q:

At 3.40, the hour hand and the minute hand of a clock form an angle of:

A) 110	B) 120
C) 130	D) 140

Answer & Explanation Answer: C) 130

Explanation:

Angle traced by hour hand in 12 hrs. = 360º.

Angle traced by it in $\frac{11}{3}$ hrs = ${(\frac{360}{12} \times \frac{11}{3})}^{0}$ = $110^{0}$

Angle traced by minute hand in 60 min. = $360^{0}$

Angle traced by it in 40 min = ${(\frac{360}{60} \times 40)}^{0}$ = $240^{0}$

$\therefore$ Required angle (240 - 110)º = $130^{0}$

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