Let the first number = x
So, the second number = 5x
Now given, if 21 is added to both the number then one of the new number becomes twice the other new number
=> 5x + 21 = 2(x + 21)
=> 5x + 21 = 2x + 42
=> 5x + 21 - 2x = 42
=> 3x + 21 = 42
=> 3x = 42 - 21
=> 3x = 21
=> x= 21/3
=> x = 7
So, the first number = x = 7
and the second number = 5x = 5*7 = 35