Multiple Choice Questions

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 7th March 2020 Shift-3

- We are given three natural numbers in the ratio 1 : 2 : 4.

- Let the numbers be $x, 2 x,$ and $4 x$ .

- The sum of their squares is given as $x^{2} + (2 x)^{2} + (4 x)^{2} = 1029$ .

- This simplifies to $x^{2} + 4 x^{2} + 16 x^{2} = 1029$ .

- Combine like terms: $21 x^{2} = 1029$ .

- Solving for $x$ , we get $x^{2} = 49$ , so $x = 7$ .

- The numbers are $7, 14,$ and $28$ .

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

Answer: Option 2 (21)

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