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

Solution:

Given, three numbers are in the ratio 1 : 2 : 3

The sum of their cubes is 4500.

We have to find the numbers.

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

According to the question,

x³ + (2x)³ + (3x)³ = 4500

x³ + 8x³ + 27x³ = 4500

36x³ = 4500

x³ = 4500/36

x³ = 500/4

x³ = 125

Taking cube root,

∛x³ = ∛125

= ∛(5)³

So, x = 5

Now, 2x = 2(5) = 10

3x = 3(5) = 15

Therefore, the required numbers are 5, 10 and 15.

✦ Try This: Three numbers are in the ratio 2:4:6 and the sum of their cubes is 7776. Find the numbers.

☛ Also Check: NCERT Solutions for Class 8 Maths

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NCERT Exemplar Class 8 Maths Chapter 3 Problem 119

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

Summary:

Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. The numbers are 5, 10 and 15.

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