Direction: Four colours namely Blue, Green Red and White are used to paint a cube such that each face is painted in exactly one colour and each colour is painted on at least one face. The cube is now cut into 120 identical pieces by making least number of cuts.
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What is the ratio of maximum and minimum number of cuboids with red colour on them?
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- 18 : 7
- 18 : 5
- 16 : 5
- None of these
Correct Option: B
For least number of cuts 120 = 4 x 5 x 6 i.e number of cuts must be 3, 4 and 5 in three planes in this case number of cubes on a face is either 6 x 5 = 30 or 6 x 4 = 24 or 4 x 5 = 20 cubes . And number of cuboids on an edge is 4 or 5 or 6
Maximum number of cuboid with red colour is possible when cube is painted with red colour in 3 sides with minimum number of common edges (which is equal to 2)
Hence required maximum value is 6 (5 + 5 + 4 - 2) = 72
For minimum number of such cuboid Red colour is used only once and minimum number of cubes in that case is 20
Hence required ratio is 72 : 20 = 18 : 5
