Question

Three no. are in a ratio of 2 3 4 if their cube is 33125 find the no.​

Answer 1

$\huge\mathbb\fcolorbox{Green}{violet}{♡correct \: Question}♡$

There numbers are in the ratio 2 : 3 : 4. If their sum of cube is 33957. Find the numbers.

$\huge\mathbb\fcolorbox{Green}{violet}{♡solution}♡$

Let the unknown number be x

The ratio becomes 2x:3x:4x

(2x)³+(3x)³+(4x)³=33957

8x³+27x³+64x³=33957

99x³=33957

x³=33957/99

x³=343

x=cube root 343

x=7

2x=2×7=14

3x=3×7=21

4x=4×7=28

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Answer 2

Appropriate Question :

Three numbers are in the ratio 2:3:4. If the sum of their cube is 33957. Find the numbers.

$\huge{\underline{\mathtt{\red{A} \pink{N} \green{S} \blue{W} \purple{E} \orange{R}}}}$

$\sf\green{Given :}$

➣ The ratio of the Three numbers = 2:3:4

➣ The Sum of the their cubes = 33957

$\sf\pink{To \: Find :}$

➣ The three Numbers

$\sf\red{Solution :}$

➪ Let, the First number = 2x

➪ Let, the Second number = 3x

➪ Let, the third number = 4x

➤ It is Given that the sum of the cubes of 2x + 3x + 4x = 33957

⇒(2x)³ + (3x)³ + (4x)³ = 33957

⇒8x³ + 27x³ + 64x³ = 33957

⇒99x³ = 33957

⇒x³ = $\frac{33957} {99}$

⇒x³ = 343

⇒x = $\sqrt[3]{343}$

⇒x = 7

$→$ The first number = 2x = 2 × 7 = 14

$→$ The second number = 3x = 3 × 7 = 21

$→$ The third number = 4x = 4 × 7 = 28

➙$\sf\blue{ So, \:the \:three \:numbers\: are \:14, 21 \:and \:28}$