# 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) 57.5 degrees | B) 67.5 degrees |

C) 77.5 degrees | D) 87.5 degrees |

Explanation:

Angle traced by hour hand in$\frac{21}{4}$ 21 hrs = ${\left(\frac{360}{12}\times \frac{21}{4}\right)}^{0}$ =$157\frac{{1}^{0}}{2}$

Angle traced by min. hand in 15 min = ${\left(\frac{360}{12}\times 15\right)}^{0}$ = ${90}^{0}$

Required Angle = ${\left(157\frac{1}{2}\right)}^{0}-{90}^{0}$ = $67\frac{{1}^{0}}{2}$

A) 11 4/11 | B) 13 4/11 |

C) 15 4/11 | D) 16 4/11 |

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.

15 min. are gained in

= (60/55 x 15)min

=16+4/11

The hands are coincident at 16 + 4/11 min past 3

A) 80 Degrees | B) 75 Degrees |

C) 60 Degrees | D) 105 Degrees |

Explanation:

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

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

Therefore, Required angle = (255 - 180) = ${75}^{o}$

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) 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) 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) 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) 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}