Question

the sum of cubes of three numbers which are in ratio 1 ratio 2 ratio 3 is 972 find the number

Answer 1

numbers are in the ratio 1:2:3

$(1 {x})^{3} + (2 {x})^{3} + ({3x})^{3} = 972$

x^3 + 8x^3 + 27x^3=972

x^3(1+8+27)=972

x^3(36)=972

x^3=972/36

x^3=27

taking cube root of 27

x=3

so the numbers are
x:2x:3x
3:6:9