Three numbers are in the ratio 2 : 3 : 4. If the sum of their cubes is 21384,…
2022
Three numbers are in the ratio 2 : 3 : 4. If the sum of their cubes is 21384, then the largest number is -
- A.
12
- B.
24
- C.
36
- D.
48
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Correct answer: B
Let the three numbers be 2x, 3x, and 4x.
Given sum of cubes: (2x)^3 + (3x)^3 + (4x)^3 = 21384
8x^3 + 27x^3 + 64x^3 = 21384
99x^3 = 21384
x^3 = 216, so x = 6.
Largest number: 4x = 4 × 6 = 24.