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Ratio of three number are 2:3:4 and sum of their cubes is 33957. Find the greatest number.

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Ratio of three number are 2:3:4 and sum of their cubes is 33957. Find the greatest number.

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Let three number are 2x, 3x and 4x 

According to question, 

(2x)3 + (3x)3 + (4x)3 = 33957 

⇒ 8x3 + 27x3 + 64x3 = 33957 

⇒ 99x3 = 33957 

⇒ x3 = 3957/99 

⇒ x3 = 343 

⇒ x3 = 7 x 7 x 7 = (7)3 

⇒ x = 3√(7)3 = 7 

Therefore, the greatest number = 4x = 4 x 7 = 28

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