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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?


Answer :

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.

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