Question

Three Numbers Are In The Ratio 2 : 3 : 5 . If Sum of Their Cubes Is 34560; Find The Numbers.


( Please Give Answer With Explanation )

Answer 1

Let the numbers be 2x,3x,5x
Therefore 2x cube+ 3x cube+ 4x cube= 34560
= 8x+ 27x+ 125x= 34560
= 160x= 34560
X= 34560/160
= 216
216 is cube root of 6
Therefore numbers are 6*2=12
3*6=18
5*6=30
Therefore numbers are 12,18,30
Hope it helped

Answer 2

Answer:

$12,18,30$

Step-by-step explanation:

• Given data:

• Three numbers are in the ratio $2:3:5$ and sum of their cubes is $34560$

• Let the three numbers be $2x,3x$ and $5x$

• According to the given data

$(2x)^{3}+(3x)^{3}+(5x)^{3}=34560$

$\Rightarrow 8x^{3} +27x^{3}+125x^{3} =34560$

$\Rightarrow 160x^{3}=34560$

$\Rightarrow x^{3} =216$

$\Rightarrow x=6$

• Therefore, the numbers are $2(6),3(6),5(6)=12,18,30$

Hence, the numbers are $12,18,30$.