Mastering Clock Reasoning Questions: Concepts, Examples, and Tips

Mastering Clock Reasoning Questions for Competitive Exams

The Clock Reasoning section is a crucial and scoring part of many competitive exams. While the questions might appear straightforward, they are often crafted to test your analytical skills in a tricky way. Understanding the key concepts thoroughly can help you solve these questions efficiently. This topic frequently appears in exams like UPSC, SSC, Railways, RBI Grade B, SBI PO, SBI Clerk, IBPS PO, IBPS Clerk, among others.

In this article, we’ll delve into the essential Clock Reasoning concepts, along with solved examples, practice questions, and handy tips and tricks. By the end, you’ll be well-prepared to tackle Clock Reasoning questions in any government exam. Let’s clear up all your doubts regarding this important topic.

What is the Clock Reasoning Section?

A clock is an instrument used to indicate and maintain time. It is a device that displays the passage of hours, minutes, and seconds. In the Clock Reasoning section, you may encounter questions related to the angle between the hands of a clock, the position of the hands, faulty clocks, and more.

Before diving into specific problem types, it’s essential to understand some basic principles about clocks:

• A clock is a complete circle, representing 360 degrees.
• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 hour = 3600 seconds

A clock has three hands: the hour hand, minute hand, and second hand. Here’s a quick breakdown:

Understanding these basics will help you solve clock reasoning questions more effectively.

Types of Clock Reasoning Questions

Now that we have an understanding of what Clock Reasoning questions entail, let’s explore the various types of Clock Reasoning questions that commonly appear in competitive exams:

1. Angle-Based Clock Problems

In this type of question, you are given a specific time, and you need to calculate the angle between the hour hand and the minute hand at that time. To solve these questions, a solid understanding of the angles traced by the different hands of the clock is essential.

2. Reflection of Clock

These questions require you to determine the time shown on a clock as seen in its mirror or water reflection. The concept of symmetry and reflection is key to solving these problems.

3. Defective Clock

In defective clock questions, you’ll encounter a clock that shows an incorrect time. You need to figure out how much the clock is gaining or losing compared to the actual time. For example, if a clock shows 4:10 when the correct time is 4:00, the clock is gaining time. Conversely, if it shows 4:40 when the correct time is 5:00, the clock is losing time.

Tips and Tricks for Solving Clock Reasoning Questions

Here are some effective tips and tricks to help you tackle Clock Reasoning questions:

Tip 1: Angle Calculation Formula

To find the angle between the hands of a clock, use the formula: θ={30H−[11M/2]}​​ Where:

• H is the hour,
• M is the minutes,
• θ is the angle between the clock’s hands.

This formula helps in quickly calculating the angle at any given time.

Tip 2: Coincidence of Hands

When the hour and minute hands coincide, they form a 0° angle. This happens once every hour except between 11:00 to 1:00 (AM/PM). There are 11 such coincidences in 12 hours and 22 in a full day. The first coincidence is at 12:00, and the next happens at 1:05.

Tip 3: Mirror Image of Time

For a 12-hour clock, to find the mirror image of a given time, subtract the given time from 11:60. For a 24-hour clock, subtract the given time from 23:60. This helps in determining what the time would look like in a mirror.

Mirror Image of Clocks

1. If the time is between 1:01 to 10:59. Then subtract from 11:60
2. If the time is between 11:01 to 12:59. Then subtract from 23:60
3. If the time is exactly an Hour then subtract from 12

Tip 4: Water Image of Time

In a water reflection:

• If the minutes are less than 30, subtract the given time from 18:30.
• If the minutes are more than 30, subtract the given time from 17:90.

This will give you the time as seen in a water reflection.

Common Clock Reasoning Questions

The below table summarizes the positions of the hour and minute hands of a clock within a 12-hour period, along with the corresponding angles and the frequency of these occurrences.

Explanation:

1. Coincident (Overlap): The hour and minute hands overlap 11 times in 12 hours.
2. Right Angle (90°): The hands form a 90° angle 22 times in 12 hours (11 times clockwise and 11 times counterclockwise).
3. Opposite (Straight Line in Opposite Directions): The hands are 180° apart (opposite directions) 11 times in 12 hours.
4. Straight Line (0° or 180°): A straight line occurs either at 0° (overlap) or 180° (opposite), totaling 22 occurrences in 12 hours.

This table is useful for understanding the patterns of a clock’s hands throughout the day.

These concepts and tips will be invaluable as you prepare for Clock Reasoning questions in your upcoming exams. Make sure to practice regularly to solidify your understanding!

Sample Clock Reasoning Questions

Question 1:

At what time between 5 and 6 o’clock will the hands of a clock coincide?

Solution: The hands of a clock coincide when the angle between them is 0°.

Question 2:

At what time between 2 and 3 o’clock will the hands of a clock form a right angle?

Solution:

Answer: The hands will form a right angle at approximately 5 minutes 27 seconds past 2.

Question 3:

How many times in a day do the hour and minute hands of a clock form a straight line but point in opposite directions?

Solution: The hour and minute hands form a straight line (180°) but point in opposite directions 11 times every 12 hours.

In 24 hours, this happens: 11×2=22 times

Answer: The hands form a straight line but point in opposite directions 22 times in a day.

Question 4:

At what time between 8 and 9 o’clock will the hands of the clock be at right angles?

Solution: Let the time be x minutes past 8.

Since 60 minutes is exactly 9:00, the valid time is:

Answer: The hands will be at right angles at approximately 27 minutes 16 seconds past 8.

Question 5:

When seen through a mirror, a clock shows 11 : 20. The correct time is

To find the correct time when the mirror image of a clock shows 11:20, we subtract the given time from 12:00.

Given:

• Mirror image time: 11:20

Solution:

Answer: The correct time is 12:40 AM.

Question 6:

By looking in a mirror, it appears that it is 9 : 30 in the clock. What is the real time?

To find the real time when the mirror image of a clock shows 9:30, you subtract the given time from 12:00.

Given:

• Mirror image time: 9:30

Answer: The real time is 2:30.