# 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) 197 1/2 | B) 167 1/2 |

C) 157 1/2 | D) 187 1/2 |

Explanation:

Angle traced by hour hand in 125/12 hrs = (360/12 * 125/12) = $312\frac{{1}^{0}}{2}$

Angle traced by minute hand in 25 min = (360/60 * 25) = ${150}^{0}$

Reflex angle = ${360}^{0}-{\left(312\frac{1}{2}-150\right)}^{0}={360}^{0}-162\frac{{1}^{0}}{2}=197\frac{{1}^{0}}{2}$

A) 10 : 27 : 41 AM | B) 8 : 51 : 04 AM |

C) 9 : 45 : 15 PM | D) 10 : 23 : 20 PM |

Explanation:

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

A) 32 8/11 | B) 33 8/11 |

C) 34 8/11 | D) 35 8/11 |

Explanation:

55min spaces are covered in 60min

60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.

loss in 64min=(65+5/11)- 64 =16/11

Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.

A) 3:15 2/8 | B) 3:49 |

C) 3:49 1/11 | D) 3:51 |

Explanation:

On straight line means 180 degree angle.

180 = 11/2 min – 30 hrs

180 = 11/2 m – 30 × 3

180 = 11/2 m – 90

(180 + 90) 2 = 11 m

m = 540/11 = 49 1/11 minutes.

A) 16 deg | B) 80 deg |

C) 88 deg | D) 94 deg |

Explanation:

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minute, the minute hand gains 330° over the hour hand.

∴ In 16 minutes, the minute hand gain over the hour hand by

A) 4pm | B) 5pm |

C) 6pm | D) 7pm |

Explanation:

Time from 7 am to 4.15 pm = 9 hrs 15 min = $\frac{37}{4}$ hrs

3 min. 5 sec. of this clock = 3 min. of the correct clock.

Now 3min.5sec. is$\frac{37}{720}$ hrs of this clock = 3 min.is$\frac{1}{20}$ hrs of the correct clock

$\frac{37}{4}$ hrs of clock = $\left(\frac{1}{20}\times \frac{720}{37}\times \frac{37}{4}\right)$ hrs of the correct clock.

= 9 hrs of the correct clock.

The correct time is 9 hrs after 7 am. i.e., 4 pm.

A) 3:16 7/11 | B) 3:16 11/4 |

C) 3:30 | D) 3:16 4/11 |

Explanation:

Coincide means 00 angle.

This can be calculated using the formulafor time A to B means ** [11m/2 - 30 (A)]**

Here m gives minutes after A the both hands coincides.

Here A = 3, B = 4

0 =11m/2 –30 × 3

11m = 90 × 2 = 180

m= 180/11 = 16 ^{4}/_{11}

So time = 3 : 16 ^{4}/_{11}

A) 80 deg | B) 160 deg |

C) 140 deg | D) 135 deg |

Explanation:

As minute hand covers, 60 degrees

Minute hand covers 4800/60 = 80°