2.A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other number. What are the numbers?

Let the number be x.
And the other number be y

As given y= 5x and also,

Condition I: x + 21 and 5x + 21

Let the number y be twice of x

Condition II: 5x + 21 = 2 (x + 21)

\(\Rightarrow\) 5x + 21 = 2x + 42 (Solving the bracket)

\(\Rightarrow\) 5x – 2x = 42 – 21 (Transposing 2x to LHS and 21 to RHS)

\(\Rightarrow\) 3x = 21

\(\Rightarrow\) x = 21 ÷ 3 = 7 (Transposing 3 to RHS)

Hence, the required numbers are 7 and 7 × 5 = 35.