Examples of mirror and water reflections are shown in the figures below: [Figure: '6a' shown with its MIRROR REFLECTION as a horizontally flipped '6a'; '6' shown with its WATER REFLECTION as a vertically flipped '6'] An object appears as the following image after first reflecting in a mirror and then reflecting on water. [Image shown: 5:24 (in seven-segment display style)] The original object is A. h2:5 B. 2:5d C. P5:2 D. h:25

GATE 2024 · General Aptitude · Mirror Image · medium

Answer: The original object is h2:5, which is option A.

  1. Establish the transformation rule: Mirror (horizontal flip) followed by water (vertical flip) equals a 180-degree rotation. Therefore: given_image = rotate_180(original), which means original = rotate_180(given_image).
  2. Read the given image: The displayed image after both reflections is: 5:24 (in a seven-segment / digital clock style). The characters from left to right are: '5', ':', '2', '4'.
  3. Rotate the given image 180 degrees: Rotating '5:24' by 180 degrees: (1) reverse the order of characters: '42:5'; (2) rotate each character 180 degrees in the seven-segment style. '4' rotated 180 degrees -> 'h' (resembles an h-shape in segment display); '2' rotated 180 degrees -> '2' mirrored (resembles the letter shape in the display); ':' stays ':'; '5' rotated 180 degrees -> 'S' or the digit '5' shape that matches. In the display convention used: the result reads h2:5.
  4. Match against options: The rotated result is 'h2:5'. Comparing with the options: A. h2:5 — matches exactly. B. 2:5d — does not match. C. P5:2 — does not match. D. h:25 — does not match.