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  4. A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 6 more than half of the original number. Find the difference of the digits of the given number.

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Q. A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 6 more than half of the original number. Find the difference of the digits of the given number.

Pair of Linear Equations in Two Variables

Solution:

Let the two-digit number be $10 x+\gamma$
Given, $10 x+y=7(x+\gamma)$
$\Rightarrow 3 x=6 \gamma \Rightarrow x=2 \gamma$
Also, $10 y+x=\frac{1}{2}(10 x+y)+6$
$\Rightarrow-8 x+19 y=12$
$\Rightarrow-16 y+19 y=12 (\because \text { from Eq. (1)) }$
$\Rightarrow y=4 \text { and } x=8 $
$\therefore x-y=4$