Multiple choice

The dimensions of a rectangular box are in the ratio 4: 3: 2 and the difference between the cost of covering it with a sheet of lead at Rs.8 and Rs.10 per square metre is 234. Find the volume of the box.

  1. 90 cubic unit

  2. 96 cubic unit

  3. 58.5 cubic unit

  4. 60 cubic unit

  5. 81 cubic unit
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let dimensions be 4k, 3k, 2k. Surface area at cost Rs.10 is SA₁ and at Rs.8 is SA₂. The cost difference equation is 10×SA₁ - 8×SA₂ = 234. When the box scales proportionally, surface area scales by k². Solving gives k²=16/9 and volume V=81 cubic units. The solution requires balancing the surface area ratios with the given cost differential.

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