Let x and y be the two numbers.

according to the question,
If 2 is added to each of two given numbers, their ratio becomes 1:2.
=> ( (x + 2) / ( y+2) ) = 1/2
=> 2x – y = – 2
=> y = 2x + 2…………………………………………….(1)

if 4 is subtracted from each of the given numbers, the ratio becomes 5:11.
=> ( ( x – 4 ) / ( y-4 ) ) = 5 /11
=> 11x – 5y= 24………………………………………(2)

substituting the value of y from eq (1) in eq(2) , we get
=> 11 x – 5( 2x+2) = 24
=> 11x – 10x  = 34
=> x= 34

y = 2x + 2
=> y = 2(34) +2 = 68 + 2
=> y = 70