Question

Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the numbers.

Answer 1

Let the ratio 1:2:3 as x, 2x and 3x

According to the question,

x3 + (2x)3 + (3x)3 = 98784

x3 + 8x3 + 27x3 = 98784

36x3 = 98784

x3 = 98784/36

= 2744

x = ∛2744 = ∛(2×2×2×7×7×7)

= 2×7 = 14

So, the numbers are,

x = 14

2x = 2 × 14

= 28

3x = 3 × 14

= 42