Question

A two-digit number is 6 less than $(\frac{3}{5}{)}^{th}$ of number formed by reversing the digits of original number. Form the linear equation in two variable.

• A. $47x-25y+30=0$, Where $xy$ is original number.
• B. $40x-25y+30=0$, Where $xy$ is original number.
• C. $47x-25y+30=0$, Where $yx$ is original number.
• D. All of the above.

Answer 1

The correct option is A $47x-25y+30=0$, Where $xy$ is original number.

Let $xy$ be the original number.
And $yx$ be number formed by reversing the digit.

According to question, two-digit original number $xy$ is $6$ less than $\frac{3}{5}yx$
$\Rightarrow xy=\frac{3}{5}yx-6\Rightarrow y+10x=\frac{3}{5}(x+10y)-6\Rightarrow y+10x=\frac{3x+30y-30}{5}\Rightarrow 5y+50x=3x+30y-30\Rightarrow 47x-25y+30=0$

This is the required equation for above situation.