Question

if 2 is added to each of two given number the ratio becomes 1 ratio 2however if 4 is subtracted from each of the given number the ratio becomes 5 ratio 11 find the numbers.
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Answer 1

Hello,

Let the two numbers be x and y
Now,

Case 1
${ \frac{x + 2}{y + 2} } = \frac{1}{2} \\ \\ 2(x + 2) = y + 2 \\ 2x + 4 = y + 2 \\ 2x - y = 2 - 4 \\ 2x - y = ( - 2)..........(1)$
Now,

Case 2
$\frac{x - 4}{y - 4} = \frac{5}{11} \\ \\ 11(x - 4) = 5(y - 4) \\ 11x - 44 = 5y - 20 \\ 11x - 5y = 44 - 20 \\ 11x - 5y = 24.........(2)$

From equation 1
We multiply 5
So the first equation become
$5(2x - y) = 5( - 2) \\ 10x - 5y = ( - 10) ............(3)$
Now,
Subtracting the two equations

$11x - 5y = 24 \\ 10x - 5y = ( - 10) \\ - \: \: \: \: + \: \: \: \: \: \: \: + \\ = = = = = = = = = = = = \\ x = 34$

Now
Obtaining y
$2x - y = ( - 2) \\ y = 2x + 2 \\ y = 2 \times 34 + 2 \\ y = 68 + 2 = 70$
So,
The two numbers are

34 and 70

Hope this will be helping you ✌️