Question

Three numbers are in the ratio 1:2:3 . The sum of their cubes is 7776. Then difference between the biggest and smallest number is?

Answer 1

Let the numbers are x, 2x and 3x.As they are in the ratio 1:2:3
Given:x3+(2x)3+(3x)3=98784
⇒x3+8x3+27x3=98784
⇒36x3=98784

⇒x3=9878436=2744

⇒x3=14×14×14
⇒x=3√14×14×14=14
⇒2x=28 and 3x=42.
∴ The required numbers are 14, 28 and 42.
Then difference between the biggest and smallest number =3x-x=2x=28 or (42-14=28)