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Time for Specific Angle

Time for Specific Angle problems ask you to find the time(s) when the clock hands form a specified angle (other than 90° or 180°). These problems generalize the right angle concept to any angle value.

10Worksheets
200+Practice Questions
AdvancedDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Time for Specific Angle

Time for Specific Angle problems ask you to find the time(s) when the clock hands form a specified angle (other than 90° or 180°). These problems generalize the right angle concept to any angle value.

Prerequisites

Angle formula: θ = |30H - 5.5M| Solving linear equations with absolute value Understanding of two solutions per hour Modular arithmetic
Why This Matters: Time for Specific Angle problems appear in 1-2 questions in advanced exams. They test equation solving and generalization skills.

How to Solve Time for Specific Angle Problems

1

Step 1: Set up the equation |30H - 5.5M| = θ, where θ is the given angle

2

Step 2: Solve for M in terms of H: M = (30H ± θ)/5.5

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Step 3: For each hour H (0 to 11, where 0=12), calculate both solutions

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Step 4: Keep only solutions where 0 ≤ M < 60

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Step 5: Format each solution as H:MM (with H=0 displayed as 12)

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Step 6: If multiple solutions exist, list all that fall within the specified range

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Step 7: Answer with the time(s)

Pro Strategy: For a given angle θ, solve M = (30H ± θ)/5.5 for each H. The ± gives two possible times per hour (except when one solution is negative or ≥60). The formula works for any θ between 0° and 180°.

Example Problem

Example: At what time between 2:00 and 3:00 do the hands form a 60° angle? Solution: Step 1: H=2, |60 - 5.5M| = 60 Step 2: Case 1: 60 - 5.5M = 60 → M = 0 (2:00) Step 3: Case 2: 60 - 5.5M = -60 → -5.5M = -120 → M = 120/5.5 = 21.818 ≈ 22 minutes Step 4: 2:00 is the start, so between 2-3, answer is 2:22 Answer: Approximately 2:22

Pro Tips & Tricks

  • For θ < 180°, there are exactly two solutions per hour (except at boundaries)
  • The formula M = (30H ± θ)/5.5 gives times in minutes past the hour
  • For H from 0 to 11, calculate both M values
  • If M < 0, discard; if M ≥ 60, discard
  • When H=0, treat as 12:00 for display
  • The same angle appears twice per hour (once with minute hand ahead, once behind)

Shortcut Methods to Solve Faster

M₁ = (30H - θ)/5.5, M₂ = (30H + θ)/5.5
If M₁ < 0, it belongs to previous hour
If M₂ ≥ 60, it belongs to next hour
For θ = 180°, M = (30H ± 180)/5.5 → only one valid per hour
The time difference between the two solutions is (2θ)/5.5 minutes

Common Mistakes to Avoid

Forgetting to check both positive and negative cases
Not verifying that M is between 0 and 60
Using 12-hour format incorrectly for H=0
Assuming only one solution per hour (there are usually two)

Exam Importance

Time for Specific Angle is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
0-1 questions
CAT
1-2 questions
INSURANCE
0-1 questions

Ready to Master Time for Specific Angle?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now