Let the two numbers be x and y

According to first condition,

x=5y ……(1)

21 is added to both the numbers

Therefore we have (x+21) and (y+21)

According to second condition

x+21=2(y+21)

From equation (1)

5y+21=2y+42

5y-2y=42-21

3y=21

y=7

Substituting y=7 in eq(1) , we get

x=5(7)

x=35

Hence the two numbers are 7 and 35