Question

A positive number is $5$ times the another number. If $21$ is added to both the numbers, then the larger number becomes twice the smaller number. What are the numbers?

• A. The required numbers are $4$ and $25$.
• B. The required numbers are $7$ and $35$.
• C. The required numbers are $9$ and $20$.
• D. The required numbers are $12$ and $28$.

Answer 1

Answer: (B)

The required numbers are $7$ and $35$.

Let the numbers be $x$ and $5x$ . It is given that
$2(x+21)=5x+21\Rightarrow 2x+42=5x+21\Rightarrow 2x-5x=21-42\Rightarrow -3x=-21\Rightarrow \frac{-3x}{-3}=\frac{-21}{-3}\Rightarrow x=7$
Hence, the required numbers are $7$ and $35$.