Three numbers are in the ratio 1: 2: 3 and the sum of their cubes is 4500. What are the numbers?

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5, 10, 15

10, 20, 30

5, 15, 25

10, 25, 35

answer is A.

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Detailed Solution

Three numbers are in the ratio 1:2:3.
For a real number a,

a 3 = a × a × a

.
Consider the numbers to be x, 2x, and 3x.
Create the equation and find x, by applying the condition.

⇒ x 3 + 2 x 3 + 3 x 3 = 4500 ⇒ x 3 + 8 x 3 + 27 x 3 = 4500 ⇒ 36 x 3 = 4500 ⇒ x 3 = 125 ⇒ x = 5

First number, x = 5.
Second number, 2(x) = 2(5) = 10.
Third number, 3(x) = 3(5) = 15.
Therefore, the required numbers are 5, 10, 15, if they are in the ratio 1: 2: 3 and the sum of their cubes is 4500.
Hence, option 1 is correct.

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