A cylinder has two concentric identical metal plates placed on each other that have identical circular holes as shown in the figure (shaded area). The plate A rotates in clockwise direction at 15° per second. The plate B rotates in anti-clockwise direction at 5° per second. If the starting positions of the plates as seen from the top of the cylinder are as shown below, the first instance when both the shaded regions completely coincide happens at:

Correct option is A

Given:
Plate A rotates clockwise at 15°/s
Plate B rotates anticlockwise at 5°/s
Initial angle between shaded holes: Let's determine this precisely from the diagram.

Key Observations from the Diagram:

Plate A’s hole is at the top (12 o’clock position) → angle = 0°

Plate B’s hole is at 135° clockwise from Plate A’s hole
(i.e., 3 quadrants = 90° + 45° = 135°)

Since A rotates clockwise and B anticlockwise, the relative angular speed is:

​$$15^\circ/\text{s} + 5^\circ/\text{s} = 20^\circ/\text{s}$$

Now calculate the time to realign (when shaded holes coincide):

​$$\text{Angle to align} = 225^\circ \\\ \\ \text{Time} = \frac{225^\circ}{20^\circ/\text{s}} = 11.25 \text{ seconds}$$​​

Correct Answer: (A) 11.25 seconds