Question

the three numbers are in ratio 3 : 4:5. the sum of their cubes is 27000.find the numbers

Answer 1

let three numbers be 3x , 4x and 5x which maintains ratio of 3: 4: 5 , so that ( 3x )3 + ( 4x)3 + ( 5x)3 = 27000 , that is 27x3 + 64x3+ 125x3 = 27000 , so 216x3 = 27000 , therfore x3 = 27000/216 =125 , so x = ( 125)1/3= 5 .Thus the numbers are 3 ( x ) =15 , 4( x ) = 20 and 5( x ) = 25 respectively

Answer 2

Answer:

The three numbers are 15, 20, 25

Step-by-step explanation:

Given the three numbers which are in ratio 3:4:5 and their sum of cubes is 27000.

we have to find the numbers.

$\text{Let the three numbers are 3x, 4x, 5x so that their ratio is 3:4:5}$

As their sum of cubes is 27000  

$(3x)^3+(4x)^3+(5x)^3=27000$

$27x^3+64x^3+125x^2=27000$

$216x^3=27000$

$x^3=\frac{27000}{216}=125$

Taking cube root on both sides, we get

$x=5$

$3x=3\times 5=15, 4x=4\times 5=20, 5x=5\times 5=25$

Hence, the three numbers are 15, 20, 25