Question

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

Answer 1

Answer:

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Answer 2

Given:

Sum of the cubes of the three numbers is 4500.

The numbers are in the ratio 1:2:3.

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To find:

The three numbers.

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Solution:

Let the first number be x.

Let the second number be 2x.

Let the third number be 3x.

So,

Cube of first number = x³

Cube of second number = (2x)³ = 8x³

Cube of third number = (3x)³ = 27x³

Now,

We are given that sum of their cubes is 4500. So the equation formed will be as follows,

x³+8x³+27x³ = 4500

36x³ = 4500

${x}^{3} = \dfrac{4500}{36}$

x³ = 125

$x = \sqrt[3]{125}$

$\bf \blue {x = 5}$

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Verification:

On substituting the value of x as 5 in the equation,

x³+8x³+27x³ = 4500

(5)³+8×(5)³+27×(5)³ = 4500

125+8×125+27×125 = 4500

125+1000+3375 = 4500

4500 = 4500

LHS = RHS

Hence Verified!

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Final answer:

First number = x

= 5

Second number = 2x

= 2×5

= 10

Third number = 3x

= 3×5

= 15

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

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$\bf \red{☆NOTE:}$ Kindly refer to the above attachment for a better understanding.