Question

three numbers are in the ratio 1:3:5 and the sum of their cubes is 0.078336. find the three numbers

Answer 1

Let the common multiple be x

so numbers will be x , 3x & 5x

by the condition given in your question we get equation

( x )^3 + ( 3x )^3 + ( 5x )^3 = 0.078336

x^3 + 27x^3 + 125 x^3 = 0.078336

153 x^3 = 0.078336

x^3 = 0.078336 /153

x^3 = 0.000512

x = 0.08

so numbers are

0.08 ,

3x = 0.08 × 3

= 0.24

5x = 0.08 × 5

= 0.4

so the numbers are 0.08 , 0.24 & 0.4

Answer 2

Let the 3 numbers be x, 3x and 5x respectively. Then, their cubes are x³, (3x)³ / 27x³ and (5x)³ / 125x³ respectively. Their sum = (1+27+125) x³ =153x³. But, their sum is 0.078336 as per the question. Hence,
153 x³ = 0.078336 or x³ = 0.000512 = (0.08)³ or x = 0.08.
So, the numbers are 0.08, 0.24 and 0.4 respectively.