🕒 Clock Problems in Aptitude – Tricks, Formulas & Solved Questions

🔍 Overview:

Clock problems are a common part of quantitative aptitude questions in competitive exams. These problems test your ability to calculate angles between the hands of a clock, identify mirror images, and solve puzzles related to time.

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📘 What You’ll Learn:

• Basics of clock angles
• Important formulas
• Common types of questions
• Shortcuts to save time
• Practice problems with solutions

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⏱️ 1. Basics of a Clock:

• A clock is a circle, divided into 360°
• It has 12 hours, each hour marking 30°
• Each minute is 6° (360° ÷ 60)
• The hour hand moves 0.5° per minute

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📐 2. Key Formulas:

Concept	Formula
Angle between hour and minute hands	`
Right angle between hands	Angle = 90°
Straight line (same line)	Angle = 180°
Hands overlap	Every 65 5/11 minutes
Hands opposite each other	Every 65 5/11 minutes too

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💡 3. Common Question Types:

• Angle between hands
• Mirror images
• Time when hands are together
• Time when hands are opposite
• Gaining or losing time

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🧠 4. Tips & Tricks:

• For angle-based questions, always apply |30H - (11/2)M|
• Hands are at right angle 22 times in 12 hours
• Hands are in the same straight line 22 times in 12 hours
• Avoid negative angles, always take the absolute value

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🧪 5. Sample Questions:

🧮 Q1. What is the angle between the hour and minute hands at 3:15?

Solution:
Angle = |30*3 - (11/2)*15| = |90 - 82.5| = 7.5°

🧮 Q2. At what time between 2 and 3 o’clock will the hands of the clock be opposite?

Solution:
Angle to be 180°
Apply formula: θ = |30H - (11/2)M| → Solve to get 2:43:7 (approx)

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📝 6. Practice Questions:

1. At what time between 4 and 5 will the hands be at right angle?
2. Find the angle at 10:25.
3. A clock gains 5 minutes every hour. How much time will it gain in a day?

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🎯 Ideal for Exams:

• Kerala PSC
• SSC CGL / CHSL
• RRB NTPC / JE
• Bank PO / Clerk
• UPSC Prelims CSAT

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#ClockProblems #AptitudeTricks #KeralaPSC #BankPOPreparation #SSCQuantitativeAptitude #AngleBetweenHands #AptitudeShortcuts #CompetitiveExamMaths

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📚 Related Topics:

• Time & Work
• Calendar Problems
• Speed, Distance & Time
• Number Systems