# Clocks Questions

**FACTS AND FORMULAE FOR CLOCKS QUESTIONS**

The face or dial of a watch is a circle whose circumference is divided into 6 equal parts, called minute spaces.

A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.

**1.** In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.

**2.** In every hour, both the hands coincide once.

**3.** The hands are in the same straight line when they are coincident or opposite to each other.

**4.** When the two hands are at right angles, they are 15 minute spaces apart.

**5.** When the hands are in opposite directions, they are 30 minute spaces apart.

**6.** Angle traced by hour hand in 12 hrs = 360°

**7.** Angle traced by minute hand in 60 min. = 360°.

Too Fast And Too Slow : If a watch or clock indicated 8.15, when the correct time is 8, it is said to be 15 minutes too fast.

On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

A) 144º | B) 168º |

C) 180º | D) 150º |

Explanation:

Angle traced by the hour hand in 6 hours =$\frac{{360}^{o}}{12}\times 6$ = ${180}^{o}$.

A) 165 degrees | B) 172.5 degrees |

C) 112.5 degrees | D) 125.5 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.

A) 44 | B) 54 |

C) 64 | D) 22 |

Explanation:

In 12 hours, they are at right angles 22 times.

In 24 hours, they are at right angles 44 times.

A) 90 degrees | B) 85 degrees |

C) 60 degrees | D) 45 degrees |

A) 20 | B) 21 |

C) 22 | D) 23 |

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.

A) 66 sec | B) 55 sec |

C) 36 sec | D) 24 sec |

Explanation:

For ticking 6 times, there are 5 intervals.

Each interval has time duration of 30/5 = 6 secs

At 12 o'clock, there are 11 intervals,

so total time for 11 intervals = 11 x 6 = 66 secs.

A) 1:45 in the afternoon | B) 7:45 in the evening |

C) 7:45 in the next morning | D) 1:45 in the next morning |

Explanation:

We know that the time difference between India and USA is 9 hrs 30 min.

India is 9:30 hrs ahead of USA.

Time in India = 4:15 + 9:30 = 13:45 PM.

Required Time after 18 hrs = 13:45 + 18 hrs = 7:45 AM.

Hence it is **7:45 AM on the next morning.**

A) Option A | B) Option B |

C) Option C | D) Option D |

Explanation:

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.

Then 15 min spaces are gained in = $\frac{60}{55}\times 15$ min.

Therefore, The hands are coincident at $16\frac{4}{11}$ min. past 3 o'clock.