The sum of the squares of 3 natural numbers is 1029 and they are in the proportion 1 2 4 The differe...........

Quantitative Aptitude (CGL) Ratio, Proportion

The sum of the squares of 3 natural numbers is 1029, and they are in the proportion 1 : 2 : 4. The difference between greatest

number and smallest number is:

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SSC CGL 6th March 2020 Shift-3

- Let the three numbers be $ x $, $ 2x $, and $ 4x $. They are in the ratio 1:2:4.

- The squares of these numbers sum up to 1029: $$ x^2 + (2x)^2 + (4x)^2 = 1029 $$.

- Simplify the equation: $$ x^2 + 4x^2 + 16x^2 = 1029 $$.

- This results in: $$ 21x^2 = 1029 $$.

- Solve for $ x^2 $: $$ x^2 = 49 $$.

- So, $ x = 7 $.

- The numbers are 7, 14, and 28.

- The difference between the greatest and smallest numbers is $ 28 - 7 = 21 $.

Option 2: 21 is the correct answer.

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