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Playing with Numbers — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSPlaying with Numbers3 Marks
Question
The difference between a $2-$digit number and the number obtained by interchanging its digits is $63.$ What is the difference between the digits of the number$?$
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Answer

Let the tens and unit digits of the number be $a$ and $b$ respectively.
Then, $\therefore$ Number $= (10a + b)$
$(10a + b) - (10b + a) = 63$
$\Rightarrow 10a - b - 10b - a = 63$
$\Rightarrow 9a - 9b = 63$
$\Rightarrow 9(a - b) = 63$
$\Rightarrow a - b = 7$
Therefore, the diffrerent between the digits is $7.$

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