Two natural numbers are in the ratio 3:4. The sum of their squares is 625. Find the numbers.

20,10

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15,20

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5,10

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15,10

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Solution

The correct option is B
15,20

Let the numbers be 3x and 4x.

Then $(3 x)^{2} + (4 x)^{2} = 625$

$\Rightarrow$ $9 x^{2} + 16 x^{2} = 625$

i.e., $25 x^{2} = 625$

$⟹ x^{2} = \frac{625}{25} = 25$

Since x is a natural number, x = 5.

Therefore, the numbers are $3 x = 3 \times 5 = 15$ and $4 x = 4 \times 5 = 20$ .

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