Question

A two-digit number is 6 times the sum of its digits. The number formed by reversing the digits is 25 less than the original number. Formulate the situations in simultaneous linear equations.

• A. $4x-5y=09y-9x+25=0$
• B. $5x-4y=09y-9x+25=0$
• C. $4x-5y=0y-x+25=0$

Answer 1

The correct option is A $4x-5y=09y-9x+25=0$

Let the original two digit number be $xy=10x+y$, Where $x$ is digit at tenth place and $y$ is digit at once place.

Also, on reversing the digits the number formed is $yx=10y+x$

Now, according to question original number $xy$ is 6 times $x+y$
$\Rightarrow xy=6(x+y)$
$\Rightarrow 10x+y=6(x+y)$
On simplifying we get
$\Rightarrow 10x+y=6x+6y\Rightarrow 4x=5y$
$\Rightarrow 4x-5y=0$

Also, according to next situation we get,
$\Rightarrow yx=xy-25\Rightarrow 10y+x=10x+y-25\Rightarrow 9y=9x-25\Rightarrow 9y-9x+25=0$