Question : The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are:
Option 1: 2, 3 and 5
Option 2: 10, 15 and 25
Option 3: 8, 12 and 20
Option 4: 4, 6 and 10
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Correct Answer: 8, 12 and 20
Solution :
Given: The ratio of three positive numbers is 2 : 3 : 5.
The sum of their squares is 608.
Let the number be $2x, 3x$ and $5x$.
As per the given conditions,
$(2x)^{2}+(3x)^{2}+(5x)^{2}=608$
⇒ $4x^{2}+9x^{2}+25x^{2}=608$
⇒ $38x^{2}=608$
⇒ $x^{2}=\frac{608}{38}=16$
⇒ $x^{2}=16$
⇒ $x=4$
So, the positive numbers are 8, 12 and 20.
Hence, the correct answer is 8, 12 and 20.
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