Question 33

Two numbers are such that the square of greater number is 504 less than 8 times the square of the other. If the numbers are in the ratio 3 : 4. Find the number.

Solution

Let the two numbers be 3x and 4x.

According to the question,

$$\ \ \ \left(4x\right)^2=8\left(3x^2\right)-504$$

=> $$\ \ \ 16x^2=72x^2-504$$

=>$$\ \ \ 56x^2=504$$

=>$$\ \ \ x^2=9$$

Or, x=$$\pm\ 3$$

Since, x cannot be -3, it is 3.

Therefore the numbers are 3x and 4x, which is 9 and 12.

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