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Q:

# The angle between the minute hand and the hour hand of a clock when the time is 8:30

 A) 80 Degrees B) 75 Degrees C) 60 Degrees D) 105 Degrees

Answer:   B) 75 Degrees

Explanation:

Angle traced by hour hand in $\inline&space;\frac{17}{2}$ hrs = $\inline&space;\left&space;(&space;\frac{360}{12}\times&space;\frac{17}{2}&space;\right&space;)^{o}$ = 255

Angle traced by min hand in 30 min = $\inline&space;\left&space;(&space;\frac{360}{60}\times&space;30&space;\right&space;)^{o}$ = 180

$\inline&space;\therefore$ Required angle = (255 - 180) = $\inline&space;75^{o}$

Q:

What is the ratio of 18 minutes to one hour ?

 A) 1/5 B) 3/4 C) 1/7 D) 3/10

Answer & Explanation Answer: D) 3/10

Explanation:

One hour = 60 min

18/60 = 3/10

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10 584
Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.15 is

 A) 0 B) 37.5 C) 27 D) 15

Answer & Explanation Answer: B) 37.5

Explanation:

Angle between hands of a clock

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

=> $\fn_jvn \small 30\left ( H -\frac{M}{5} \right )+\frac{M}{2}$ degrees

Here H = 4, M = 15 and the minute hand is behind the hour hand.

Hence the angle

$\fn_jvn \small 30\left ( H -\frac{M}{5} \right )+\frac{M}{2}$ = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

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10 1594
Q:

What is the angle made by the hour hand and the minute hand, if the clock shows 9:15 pm ?

 A) 165 degrees B) 172.5 degrees C) 112.5 degrees D) 125.5 degrees

Answer & Explanation Answer: B) 172.5 degrees

Explanation:

The minute hand angle is the easiest since an hour (i.e. 60 minutes) corresponds to the entire 360 degrees, each minute must correspond to 6 degrees. So just multiply the number of minutes in the time by 6 to get the number of degrees for the minute hand.
Here 15 minutes corresponds to 15 x 6 = 90 degrees

Next, you have to figure out the angle of the hour hand. Since there are 12 hours in the entire 360 degrees, each hour corresponds to 30 degrees. But unless the time is EXACTLY something o'clock, you have to write the time as a fractional number of hours rather than as hours and minutes.
Here the time is 9:15 which is (9 + 15/60) = 37/4 hours. Since each hour corresponds to 30 degrees, we multiply 30 to get (37/4)(30) = 277.5 degrees.

Since the hour hand is at 277.5 degrees and the minute hand is at 90 degrees, we can subtract to get the angle of separation. 277.5 - 90 = 187.5 =~ 360 - 187.5 = 172.5 degrees.

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7 2231
Q:

How many minutes does a watch lose per day, if its hands coincide every 64 minutes ?

 A) 36 7/9 min B) 32 8/11 min C) 34 3/11 min D) 65 5/11 min

Answer & Explanation Answer: B) 32 8/11 min

Explanation:

55 min. spaces are covered in 60 min.

60 min. spaces are covered in min. = min.

Loss in 64 min. = min.

Loss in 24 hrs = min. = min.

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7 1895
Q:

How many degrees will the minute hand move, in the same time in which the second hand move 4800 ?

 A) 80 deg B) 160 deg C) 140 deg D) 135 deg

Answer & Explanation Answer: A) 80 deg

Explanation:

As minute hand covers, 60 degrees

Minute hand covers 4800/60 = 80°

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