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