If the length , breadth and height of a room are in the ratio 4 : 2 : 1 . If…
2026
If the length , breadth and height of a room are in the ratio 4 : 2 : 1 . If the length and breadth are halved , while the height is doubled . Then the total area of the 4 walls of the room will be ?
- A.
decreased by 30 %
- B.
increased by 20 %
- C.
decreased by 15 %
- D.
there will be no change
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Correct answer: D
Answer: there will be no change
Work:
Formula: total area of the four walls = 2 × height × (length + breadth).
Let the common multiplier be x. Then length = 4x, breadth = 2x, height = 1x.
Initial area = 2 × 1x × (4x + 2x) = 2x × 6x = 12x^2.
After changes: length = 2x, breadth = 1x, height = 2x. New area = 2 × 2x × (2x + 1x) = 4x × 3x = 12x^2.
Conclusion: initial and new areas are equal (12x^2), so the total area of the four walls remains unchanged (0% change).