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Q:

At what time between 2 and 3 O'clock, the hands of a clock coincide ?

 A) 1 10/11 minutes past 2 B) 1 10/11 minutes past 3 C) 1 11/10 minutes past 3 D) 11 10/11 minutes past 2

Explanation:

Since, in one hour, two hands of a clock coincide only once, so, there will be value.
Required time $\inline \fn_jvn T=\frac{2}{11}\left ( H\times 30+A^{\circ} \right )$ minutes past H.
Here H - initial position of hour hand = 2 (since 2 O'clock)
A° = Required angle = 0° (Since it coincides)

$\inline \fn_jvn T=\frac{2}{11}\left ( 2x30+0^{\circ} \right )$ minutes past 2

=> $\inline \fn_jvn 1\tfrac{10}{11}$ minutes past 2

Filed Under: Clock puzzles
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3 34
Q:

A clock is started at 11 a.m. By 600 seconds past 6 p.m, the hour hand has turned through ?

 A) 155 degrees B) 175 degrees C) 205 degrees D) 215 degrees

Explanation:

The total angle traced by the hour hand is the angle traced in 7 hours and 10 minutes.
We know that the angle traced by the hour hand in one hour is 30º and in one minute is 1/2º.
Therefore, (30º x 7) + (10 x 1/2º) = 215º is the angle traced by the hour hand.

Filed Under: Clock puzzles
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4 49
Q:

If a Siren sounds for every 5 seconds, how many times will it sound in ¾ of an hour?

 A) 541 times B) 540 times C) 450 times D) 275 times

Explanation:

There are 60 minutes in an hour.
In ¾ of an hour there are (60 × ¾) minutes = 45 minutes.
In ¾ of an hour there are (60 × 45) seconds = 2700 seconds.
Siren sounds for every 5 seconds.
In 2700 seconds $\inline \fn_jvn \small \frac{2700}{5}$ = 540 times.

The count start after the first sound, the Siren will sound 541 times in ¾ of an hour.

Filed Under: Clock puzzles
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2 85
Q:

Calculate the angle between the two hands of clock when the clock shows 4 : 20 p.m. ?

 A) 5 degrees B) 10 degrees C) 15 degrees D) 25 degrees

Explanation:

Since at 4 : 20 the minute hand will be at 4 and the angle between them will be same as the distance covered in degree by the hour hand in 20 minutes.

Required angle = distance of hour hand = speed × time = $\inline \frac{1}{2}$ × 20 =10 degrees.

Filed Under: Clock puzzles
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