Question

Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957.find the numbers

Answer 1

Solution :-

Let The Three Numbers be 2x , 3x & 4x .

A/q,

→ (2x)³ + (3x)³ + (4x)³ = 33957

→ 8x³ + 27x³ + 64x³ = 33957

→ 99x³ = 33957

Dividing Both Sides by 99,

→ x³ = 343

cube - Root Both sides Now,

→ x = 7.

Hence, Three Number Are :-

→ 2x = 2*7 = 14 (Ans.)

→ 3x = 3*7 = 21 (Ans.)

→ 4x = 4*7 = 28 (Ans.)

Answer 2

SoluTion:

Let the numbers be 2n, 3n, 4n.

According to Question, sum of their cube is 33975.

=> (2n)³ + (3n)³ + (4n)³ = 33975

=> 8n³ + 27n³ + 64n³ = 33975

=> 99n³ = 33975

=> n³ = 33975/99

=> n³ = 343

=> n = ³√343

=> n = 7

Hence, numbers are :

• 2n = 2×7 => 14
• 3n = 3×7 => 21
• 4n = 4×7 => 28