Question : The ratio of two positive numbers is 3 : 4. The sum of their squares is 400. What is the sum of the numbers?
Option 1: 28
Option 2: 22
Option 3: 24
Option 4: 26
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Correct Answer: 28
Solution :
Let the numbers be $3x$ and $4x$.
Squares of the numbers are $9x^2$ and $16x^2$.
According to the question,
$9x^2 + 16x^2 = 400$
⇒ $25x^2= 400$
⇒ $x^2 = 16$
$\therefore x = 4$
The numbers are $(3 × 4) = 12$ and $(4 × 4) = 16$
$\therefore$ The sum of the numbers $= (12 + 16) = 28$
Hence, the correct answer is 28.
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