Question

If $1$ is added to each of the two certain numbers, their ratio is $1:2$; and if $5$ is subtracted from each of the two numbers, their ratio becomes $5:11$. Find the numbers.

• A. $35$ and $70$
• B. $35$ and $71$
• C. $35$ and $72$
• D. $35$ and $73$

Answer 1

The correct option is B $35$ and $71$

Let the numbers be $x$ and $y$
Given, if $1$ is added to the numbers, then ratio $=\frac{x+1}{y+1}=\frac{1}{2}$
$=>2x+2=y+1$
$=>2x-y=-1$ ...(1)
Also, if $5$ is subtracted from the numbers, then ratio $=\frac{x-5}{y-5}=\frac{5}{11}$

$=>11x-55=5y-25$
$=>11x-5y=30$ ...(2)

Multiplying equation $\left(1\right)$ with $5$ we get, $10x-5y=-5$ ----- equation $\left(3\right)$

Subtracting equation $\left(3\right)$from $\left(1\right)$, we get $x=35$

Substituting $x=35$ in the equation $\left(1\right)$, we get $70-y=-1=>y=71$

Hence, the numbers are $35$ and $71$