Question

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Answer 1

Let the numbers be 2x, 3x and 4x, respectively.

∵ Sum of their cubes = 0.334125  ...[Given]

According to the question,

(2x)³ + (3x)³ + (4x)³ = 0.334125

⇒ 8x³ + 27x³ + 64x³ = 0.334125

⇒ 99x³ = 0.334125

⇒ x³ = `0.334125/99`

⇒ x³ = 0.003375

⇒ x³ = `3375/1000000`

⇒ x = `root(3)((15 xx 15 xx 15)/(10 xx 10 xx 10 xx 10 xx 10 xx 10)`  ...[Taking cube root on both sides]

⇒ x = `15/(10 xx 10)`

∴ x = 0.15

Hence, the required numbers are 2 × 0.15, 3 × 0.15 and 4 × 0.15 i.e. 0.3, 0.45 and 0.6.