Question

the three numbers are in the ratio 2 3 4 and the sum of their cubes add upto 12375 find the numbers

Answer 1

Let the cubes of numbers are 2x³, 3x³ and 4x³. Now, (2x)³+ (3x)³+ (4x)³= 12375 => 8x³+ 27x³+64x³= 12375 => 99x³= 12375 => x³= 12375/99 => x³= 125 => x=5 ; The numbers are-- (A) Ist number is 2x= 2×5=10 (B) 2nd number is 3x = 3×5=15 (C) 3rd number is 4x = 4×5=20

Answer 2

let the numbers be  a, b and c.
a = 2x     b = 3x     c = 4 x

sum of their cubes = 8 x³ + 27 x³ + 64 x³ = 99 x³

so   99 x³ = 12375
            x³ = 125
             x = 5