Question

If three numbers are in the ratio 3 : 4 : 5 such that the sum of their cubes is 1728, then the cube of the middle number is
1. 216
2. 512
3. 256
4. 128

Answer 1

Correct Answer - Option 2 : 512

Given:

If three numbers are in the ratio 3 : 4 : 5

The sum of their cubes is 1728.

Calculation:

Let the three number be 3x, 4x and 5x

According to the question,

⇒ (3x)³ + (4x)³ + (5x)³ = 1728

⇒ (27 + 64 + 125)x³ = 1728

⇒ x³ = 8

⇒ x = 2

The cube 4 × 2 = 8

⇒ 8³ = 512

∴ The cube of the middle number is 512.