Question

Q20. Three numbers are in the
ratio 2:3:4. If the sum of their
cubes is 72171, then the
smallest number is *
9
18
27
36​

Answer 1

Answer:

Three numbers are in the

ratio 2:3:4. If the sum of their

cubes is 72171, then the

smallest number is *

Answer 2

Answer:

Given :-

• Three numbers are in the ratio of 2 : 3 : 4.
• The sum of their cubes is 72171.

To Find :-

• What is the smallest number.

Solution :-

Let,

$\mapsto \bf First\: Number =\: 2x$

$\mapsto \bf Second\: Number =\: 3x$

$\mapsto \bf Third\: Number =\: 4x$

According to the question,

$\bigstar$ The sum of their cubes is 72171.

$\implies \sf (2x)^3 + (3x)^3 + (4x)^3 =\: 72171$

$\implies \sf 8x^3 + 27x^3 + 64x^3 =\: 72171$

$\implies \sf 99x^3 =\: 72171$

$\implies \sf x^3 =\: \dfrac{\cancel{72171}}{\cancel{99}}$

$\implies \sf x^3 =\: 729$

$\implies \sf x =\: \sqrt[3]{729}$

$\implies \sf\bold{\purple{x =\: 9}}$

Hence, the numbers are :

❒ First Number :

$\longrightarrow \sf First\: Number =\: 2x$

$\longrightarrow \sf First\: Number =\: 2 \times 9$

$\longrightarrow \sf\bold{\red{First\: Number =\: 18}}$

❒ Second Number :

$\longrightarrow \sf Second\: Number =\: 3x$

$\longrightarrow \sf Second\: Number =\: 3 \times 9$

$\longrightarrow \sf\bold{\red{Second\: Number =\: 27}}$

❒ Third Number :

$\longrightarrow \sf Third\: Number =\: 4x$

$\longrightarrow \sf Third\: Number =\: 4 \times 9$

$\longrightarrow \sf\bold{\red{Third\: Number =\: 36}}$

${\small{\bold{\underline{\therefore\: The\: smallest\: number\: is\: 18\: .}}}}$

Hence, the correct options is option no 2) (18).