Question

three numbers are in the ratio 1 is to 2 is to 3 and the sum of their cubes is 7776 the largest number is

Answer 1

Let the numbers be x , 2x and 3x
According to the question,
x^3 + (2x)^3 + (3x)^3 = 7776
=> x^3 + 8x^3 + 27x^3 = 7776
=> 36x^3 = 7776
=> x^3 = 7776/36
=> x =
$\sqrt[3]{216}$
= 6
Therefore the largest no. = 3x = 3×6 = 18
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Answer 2

Let the numbers be 1x:2x:3x
So, their cubes will be 1x:8x:27x
Their sum will be 36x^3,
36x^3=7776
x^3=6^3
x = 6

The numbers would be
1x = 6 × 1 = 6
2x = 6 × 2 = 12
3x = 6 × 3 = 18

Ans=The greatest number is 18