Question

three number are in ratio 1:2:3 the sum of three cube is 98784 find the number

Answer 1

let the 3 no.s are 1x,2x and 3x
therafore sum of their cubes=(x)cube+(2x)cube+(3x)cube=98784
=(36x)cube
(x)cube=(98784/36)=2274
x=cube root (2744)=14

therefore the 3 nos. are 14,28,42

Answer 2

Since the numbers are in the ratio 1:2:3, let the numbers be x,2x and 3x.
Given that the sum of three cube is 98784

So  x³ + (2x)³ + (3x)³ = 98784
⇒ x³ + 8x³ + 27x³ = 98784
⇒ 36x³ = 98784
⇒ x³ = 98784 / 36 
⇒ x³ = 2274
⇒ x = ∛2274
⇒ x = 14

2x = 2 × 14 = 28
3x = 3 × 14 = 42

So numbers are 14, 28 and 42.