Question

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

Answer 1

Let the no.s be x and y.

given, A/Q,

$x+1:y+1=1:2$

$\frac{x+1}{y+1}$= $\frac{1}{2}$

$2x+2=y+1$

$2x-y=-1$ .....(1)

Again, $x-5:y-5=5:11$

$\frac{x-5}{y-5}=\frac{5}{11}$

$11x-55=5y-25$

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

from 1 and 2, by elimination method,

$\left(1\right)\times 5\Rightarrow 10x-5y=-5$

$\left(2\right)\times 1\Rightarrow 11x-5y=30$

$-1x=-35,so,x=35$

We know, from (1)

$2x-y=-1$

putting $x==35$, we get

$2\times 35+1=y$

$71=y$

so the no.s are $30$ and $71.$