Question:
P and Q are two layered dials of a watch. Dial Q is placed on the top of dial P. The white areas in dial Q are cut portions through which parts of dial P are visible from the top. The pattern shown in image R is taken at 12:00 hrs. Dial Q rotates by 90 degrees after every 15 minutes in clockwise direction about its central axis. Dial P rotates by 45 degrees anticlockwise after every 30 minutes about its central axis. Find out the right pattern at 13:30 hrs.
P and Q are two layered dials of a watch. Dial Q is placed on the top of dial P. The white areas in dial Q are cut portions through which parts of dial P are visible from the top. The pattern shown in image R is taken at 12:00 hrs. Dial Q rotates by 90 degrees after every 15 minutes in clockwise direction about its central axis. Dial P rotates by 45 degrees anticlockwise after every 30 minutes about its central axis. Find out the right pattern at 13:30 hrs.
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When analyzing layered rotating patterns, calculate the effective rotation of each layer and combine them to determine the visible result.
Updated On: Jan 13, 2026
- A
- B
- C
- D
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The Correct Option is C
Solution and Explanation
1. Initial Configuration (12:00 hrs): The pattern \(R\) represents the initial configuration of the two dials \(P\) and \(Q\) at 12:00 hrs.
2. Rotation of Dial Q: Dial \(Q\) rotates 90 degrees clockwise every 15 minutes. Between 12:00 hrs and 13:30 hrs (1 hour and 30 minutes), \(Q\) completes:
\[ \frac{90}{15} \times 90 = 540 \text{ degrees}. \] Since \(540^\circ = 360^\circ + 180^\circ\), \(Q\) rotates by an effective 180 degrees clockwise. 3. Rotation of Dial P: Dial \(P\) rotates 45 degrees anticlockwise every 30 minutes.
Between 12:00 hrs and 13:30 hrs, \(P\) rotates: \[ 45^\circ \times \frac{90}{30} = 135 \text{ degrees anticlockwise}. \] 4. Combined Rotation Effect: The combined rotations of \(P\) and \(Q\) determine the visibility pattern. After applying these rotations:
- \(Q\) shifts 180 degrees clockwise. - \(P\) shifts 135 degrees anticlockwise. The resulting pattern aligns with Option C. Conclusion: The correct pattern at 13:30 hrs is \(C\).
2. Rotation of Dial Q: Dial \(Q\) rotates 90 degrees clockwise every 15 minutes. Between 12:00 hrs and 13:30 hrs (1 hour and 30 minutes), \(Q\) completes:
\[ \frac{90}{15} \times 90 = 540 \text{ degrees}. \] Since \(540^\circ = 360^\circ + 180^\circ\), \(Q\) rotates by an effective 180 degrees clockwise. 3. Rotation of Dial P: Dial \(P\) rotates 45 degrees anticlockwise every 30 minutes.
Between 12:00 hrs and 13:30 hrs, \(P\) rotates: \[ 45^\circ \times \frac{90}{30} = 135 \text{ degrees anticlockwise}. \] 4. Combined Rotation Effect: The combined rotations of \(P\) and \(Q\) determine the visibility pattern. After applying these rotations:
- \(Q\) shifts 180 degrees clockwise. - \(P\) shifts 135 degrees anticlockwise. The resulting pattern aligns with Option C. Conclusion: The correct pattern at 13:30 hrs is \(C\).
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