Two numbers are in the ratio 7 9 If the sum of their squares is 8320 then the sum of the two nmnbers...........

Quantitative Aptitude (MTS) Ratio, Proportion

Two numbers are in the ratio 7:9. If the sum of their squares is 8320, then the sum of the two nmnbers is:

This questions was previously asked in

SSC MTS 7th October 2021 Shift-1

128

228

120

124

- The two numbers can be expressed as $7x$ and $9x$ due to their ratio of 7:9.

- The sum of the squares of these two numbers is given: $ (7x)^2 + (9x)^2 = 8320 $.

- Simplifying the equation:

$$ 49x^2 + 81x^2 = 8320 $$

$$ 130x^2 = 8320 $$

$$ x^2 = \frac{8320}{130} = 64$$

$$ x = 8 $$

- The numbers are $7x = 56$ and $9x = 72$.

- The sum of these numbers is:

$$ 56 + 72 = 128 $$

Here are the options:

- Option 1: 128

- Option 2: 228

- Option 3: 120

- Option 4: 124

. The correct sum is $\boxed{128}$.

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