Q 2. Two numbers are in the ratio 2 : 3 and the difference of theirsquares is 320. The numbersare

Question

Two numbers are in the ratio 2 : 3 and the difference of their squares is 320.

The numbers are:

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Let's denote the two numbers as 2x and 3x, where x is a common multiplier.

According to the problem, the difference of their squares is 320.

So, we can write the equation as follows:

(3x)^2 - (2x)^2 = 320

9x^2 - 4x^2 = 320

5x^2 = 320

Now, solve for x:

x^2 = 320 / 5

x^2 = 64

x = sqrt(64)

x = 8

Now that we have the value of x, we can find the two numbers:

The first number is 2x = 2*8 = 16

The second number is 3x = 3*8 = 24

So, the two numbers are 16 and 24.

This problem has been solved

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