Question : If the ratio of two numbers is 1 : 5 and their product is 320, the difference between the squares of these two numbers is:
Option 1: 1024
Option 2: 1256
Option 3: 1536
Option 4: 1435
Correct Answer: 1536
Solution :
Let the numbers be $x$ and $5x$.
According to the question,
$x × 5x= 320$
$\Rightarrow 5x^2 = 320$
$\Rightarrow x^2 = 64$
$\Rightarrow x = 8$
So, the numbers are $8$ and $(8×5)=40$.
Now, the difference between the squares of $8$ and $40$
$= 40^2 - 8^2$
$= 1600 - 64$
$= 1536$
Hence, the correct answer is 1536.
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