# 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) 48 min. past 12. | B) 46 min. past 12. |

C) 45 min. past 12. | D) 47 min. past 12. |

Explanation:

Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.

24 hours 10 min. of this clock = 24 hours of the correct clock.

$\frac{145}{6}$ hrs of this clock = 24 hours of the correct clock.

29 hours of this clock = $24*\frac{6}{145}*29$ hrs of the correct clock

= 28 hrs 48 min of the correct clock.

Therefore, the correct time is 28 hrs 48 min. after 8 a.m.

This is 48 min. past 12.

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 |

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.

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.

A) 54 past 4 | B) (53 + 7/11) past 4 |

C) (54 + 8/11) past 4 | 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.

A) 11pm | B) 12pm |

C) 1pm | D) 2pm |

Explanation:

Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.

Now 23 hrs 44 min. of this clock = 24 hours of correct clock.

356/15 hrs of this clock = 24 hours of correct clock

89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.

= 90 hrs of correct clock.

So, the correct time is 11 p.m.

A) 24min | B) 12min |

C) 13min | D) 14min |

Explanation:

In this type of problems the formuae is

(5*x+ or - t)*12/11

Here x is replaced by the first interval of given time. Here x is 5.

t is spaces apart

Case 1 : (5*x + t) * 12/11

(5*5 + 3) * 12/11

28 * 12/11 = 336/11= $31\frac{5}{11}$ min

therefore the hands will be 3 min apart at 31 5/11 min past 5.

Case 2 : (5*x - t) * 12/11

(5*5 -3 ) * 12/11

22 *12/11 = 24 min

therefore the hands will be 3 min apart at 24 min past 5

A) 47.5 degrees | B) 57.5 degrees |

C) 45.5 degrees | D) 55.5 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°

A) 100/11 min past 8 | B) 120/11 min past 8 |

C) 90/11 min past 8 | D) 80/11 min past 8 |

Explanation:

In this type of problems the formulae is $\left(5x-30\right)\times \frac{12}{11}$

x is replaced by the first interval of given time Here i.e 8

$\left(5*8-30\right)*\frac{12}{11}$

= $\frac{120}{11}$min

Therefore the hands will be in the same straight line but not

together at $\frac{120}{11}$ min.past 8.

A) 7pm on wednesday | B) 20 min past 7pm on wednesday |

C) 15min past 7pm on wednesday | D) 8pm on wednesday |

Explanation:

This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains $5+5\frac{48}{60}$ min in a time of (7×24)+12 = 180 hours.

To show the correct time, it has to gain 5 min.

$\frac{54}{5}min\to 180hours$

5min ->

$\left(\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$\frac{54}{2}$}\right.\times 180\right)$

$83\frac{1}{3}hrs=72hrs+11\frac{1}{3}hrs=3days+11hrs+20min$

So the correct time will be shown on wednesday at 7:20 PM