All questions of Clocks for Bank Exams Exam

Understanding Clock Mechanics
To determine when the hands of a clock will coincide between 3 and 4 o'clock, we need to analyze the movement of the hour and minute hands.
Movement of the Hands
- The minute hand moves at 6 degrees per minute (360 degrees/60 minutes).
- The hour hand moves at 0.5 degrees per minute (30 degrees/60 minutes).
At 3:00, the hour hand is at 90 degrees (3 hours x 30 degrees/hour).
Setting Up the Equation
Let "t" be the time in minutes after 3:00 when the hands coincide. The positions of the hands at that time can be expressed as:
- Minute hand position: 6t degrees
- Hour hand position: 90 + 0.5t degrees
To find the time when they coincide, set their positions equal:
6t = 90 + 0.5t
Solving the Equation
1. Rearranging gives:
6t - 0.5t = 90
2. This simplifies to:
5.5t = 90
3. Solving for "t" yields:
t = 90 / 5.5 = 16.36 minutes
This can be converted into minutes and seconds.
Final Result
When we convert 16.36 minutes into minutes and seconds, we get:
- 16 minutes and approximately 22 seconds.
Thus, the hands of the clock will coincide at approximately 16 4/11 minutes past 3.
Conclusion
The correct answer is option 'A': 16 4/11 minutes past 3. This method illustrates how the positions of the clock hands can be calculated using their respective speeds and relative positions.

Angle = |(30 × H) - (5.5 × M)| = |(30 × 7) - (5.5 × 20)| = |210 - 110| = 100°.