Question

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

Answer 1

Answer:

• The numbers are 5, 10 and 15.

Step-by-step explanation:

Given,

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

To Find,

• The numbers.

Solution,

Let's,

• The first number = x

Then,

• The second number = 2x

Then,

• The third number = 3x

After Cubing the numbers,

• The first number = x³

• The second number = 8x³

• The third number = 27x³

The sum of the cubes = 4500 •••[Given]

• → x³ + 8x³ + 27x³ = 4500
• → 36x³ = 4500
• → x³ = 125
• → x = 5

The value of x is 5.

The first number = x

• The first number = 5

The second number = 2x

• The second number = 10

The third number = 3x

• The third number = 15

Required Answer,

• The numbers are 5, 10 and 15.