# Clock – Aptitude Questions and Answers

Clock questions are commonly included in quantitative aptitude exams. These questions typically require the application of basic arithmetic and algebraic concepts to solve problems related to time, such as calculating the time difference between two events, determining the time at which two hands of a clock will coincide, and calculating the speed or rate at which a clock is running.

Clock problems are often used in exams to test a candidate’s ability to reason with numbers, perform calculations accurately and quickly, and apply mathematical concepts to real-world situations. They can be a useful tool for assessing a candidate’s overall Quantitative Aptitude and problem-solving skills.

**Practice Quiz**:

## Clocks Formulas and Concepts:

Here are some formulas, concepts, and short related to clocks that are commonly used in quantitative aptitude exams:

### Minute Spaces:

A typical analog clock has a circular face with twelve-hour markings, and 60-minute markings placed around the circumference of the circle, called minute spaces.

- When it comes to telling time, clocks use two primary hands: the hour hand and the minute hand.
- Hour hand, also known as the shorthand, is typically smaller and moves more slowly than the minute hand.
- Meanwhile, the larger, faster-moving hand is called the minute hand or long hand.
- The markings on the face of a clock are 60 spaces, one each for a minute. Every hour, the minute hand completes one round of 60 spaces and the hour hand completes one full round every 12 hours.

### Important Points and Shortcuts for Clock:

- In 60 minutes, the minute hand gains 55 spaces (also known as minute spaces) over the hour hand. For example, if the initial time is 12:00, then after 1 hour, the minute hand would cover 60 spaces whereas the hour hand would cover only 5 spaces. Thus, the minute hand covers 55 spaces extra than the hour hand.
- The minute hand covers 360 degrees in 60 minutes. => In 1 minute, the minute hand covers 360 / 60 = 6 degrees
- The hour hand covers 360 degrees in 12 hours. => In 1 hour, the hour hand covers 360 / 12 = 30 degrees => In 1 minute, the hour hand covers 30 / 60 = 0.50 degrees
- The angle between the minute hand and the hour hand increases by 5.50 degrees every minute. For example, after 2 minutes, angle made by the minute hand = 2 x 6 = 12 degrees and angle made by the hour hand = 2 x 0.50 = 1 degree => Angle between the hour hand and the minute hand after 2 minutes = 12 – 1 = 11 degrees = 2 x 5.50 degrees
- In every hour, the minute hand and the hour hand coincide once.
- If the minute hand and the hour hand are in the same line, then the angle between them is either 0 degree or 180 degrees.
- The angle between the minute hand and the hour hand is 180 degrees if they are 30 spaces apart, 90 degrees if they are 15 spaces apart, and 0 degrees if they are 0 spaces apart.
- If the clock shows time ahead of the actual time, it is said to be running fast. For example, if the clock is showing 12:15 PM but it is actually 12:00 PM, then the clock is said to be running 15 minutes fast.
- If the clock shows time behind the actual time, it is said to be running slow. For example, if the clock is showing 2:15 PM but it is actually 2:30 PM, then the clock is said to be running 15 minutes slow.

## Angle Equivalence of a Minute:

Below mentioned tables contain the angular values of the first ten minutes:

Minute(s) | Angular values |

1 | 6Â° |

2 | 12Â° |

3 | 18Â° |

4 | 24Â° |

5 | 30Â° |

6 | 36Â° |

7 | 42Â° |

8 | 48Â° |

9 | 54Â° |

10 | 60Â° |

## Sample Problems on Clocks

### Q1: Find the angle between the hands of a clock at 3:20 PM.

**Solution**:

At 3:00 PM, the angle made by the minute hand = 0 degree, and the angle made by the hour hand = 3 x angle made by the hour hand in one hour = 3 x 30 = 90 degrees Now, in the next 20 minutes, angle made by the minute hand = 20 x angle made by the minute hand in 1 minute = 20 x 6 = 120 degrees and angle made by the hour hand = 20 x angle made by the hour hand in 1 minute = 20 x 0.50 = 10 degrees => Angle made by the minute hand at 3:20 PM = 0 + 120 = 120 degrees => Angle made by the hour hand at 3:20 PM = 90 + 10 = 100 degrees Therefore, the angle between the hands of the clock at 3:20 PM = 120 – 100 = 20 degrees.

Another Method: At 3:00 PM, the angle made by the minute hand = 0 degree, and the angle made by the hour hand = 3 x angle made by the hour hand in one hour = 3 x 30 = 90 degrees => Initial angle between the two hands = 90 degrees Now, we know that the difference between the two hands of the clock increases every minute by 5.50 degrees. => Difference between the hands of the clock after 20 minutes = 20 x 5.50 = 110 degrees Therefore, the difference between the two hands at 3:20 PM = 110 – 90 = 20 degrees.

### Q2: At what time between 3 PM and 4 PM would the two hands of the clock be together?

**Solution**:

At 3 PM, the hour hand would be at 15 spaces and the minute hand would be at 0 spaces. The minute hand would have to cover these extra 15 spaces in order to meet the hour hand. Now, 55 minutes are gained by the minute hand in 60 minutes. => 15 minutes would be gained in (60 / 55) x 15 = 180 / 11 minutes Thus, the two hands of the clock meet at 180 / 11 minutes past 3 PM, i.e., around 3:16:22 PM.

### Q3: How many times in a day the two hands of a clock coincide?

**Solution**:

Between 11 to 1, the hands of the clock coincide only once, i.e., at 12. At 12:00 AM and 12:00 PM, the hour hand and the minute hand do not coincide with each other So, every 12 hours, they coincide 11 times. Therefore, the two hands of the clock coincide 22 times in a day.

### Q4: At what time between 5 and 6 o’clock, do the minute and hour hands make an angle of 34 degree with each other

**Solution**:

The angle between the minute hand and the hour hand at 5 o’clock is 150 degrees.

The angle between the hands becomes 34 degrees when the angle changes by 116 degrees and 184 degrees, i.e. (150-34) and (150+34).

The angle changes by 5.5 degrees in 1 min.

The angle changes by 116 degrees in 1/5.5 x 116=21 1/11 min.

The angle changes by 184 degrees in 1/5.5 x 184=33 5/11 min.

Therefore the angle between the two hands is 34 degrees when the time is 5 hr 21 1/11 min, and again at 5 hr 33 5/11 min.

Test your knowledge of Clocks in Quantitative Aptitude with the quiz linked below, containing numerous practice questions to help you master the topic:-

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