A cube and cuboid have same volume. The dimensions of the cuboid are in the ratio \( 1: 2: 4 \)....

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A cube and cuboid have same volume. The dimensions of the cuboid are in the ratio \( 1: 2: 4 \). If the difference between the cost of polishing the cube and cuboid at the rate of \( ₹ 5 \) per \( \mathrm{m}^{2} \) is \( ₹ 80 \), then find their volumes.
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