Question

One number is greater than thrice the other number by $2.$ If $4$ times the smaller number exceeds the greater by $5$, find the numbers.

• A. $23,7$
• B. $23,8$
• C. $23,9$
• D. None of these

Answer 1

The correct option is A $23,7$

Let the greater number be $x$ and the smaller number be $y$.

According to the question,

$x-2=3y$ $.........\left(1\right)$

$4y-5=x$ $........\left(2\right)$

On adding both equations, we get

$x-2+4y-5=3y+x$

$x-7+4y=3y+x$

$x-x-7=3y-4y$

$-7=-y$

$y=7$

From equation $\left(1\right)$

$x=7\times 3+2$

$x=23$

Hence,the greater number is $23$ and the smaller number is $7$.