The ten's digit of a two-digit number is grea | vedclass

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(A) Let the two-digit number be represented as $10x + y$,where $x$ is the ten's digit and $y$ is the unit's digit.According to the problem,the ten's d

Vedclass · Accepted Answer

$81$

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(A) Let the two-digit number be represented as $10x + y$,where $x$ is the ten's digit and $y$ is the unit's digit.According to the problem,the ten's digit is $7$ more than the unit's digit: $x = y + 7$.The value of the number is $10x + y$.When the digits are interchanged,the new number becomes $10y + x$.According to the problem,subtracting $63$ from the original number gives the new number:$(10x + y) - 63 = 10y + x$$9x - 9y = 63$$x - y = 7$Substitute $x = y + 7$ into the equation:$(y + 7) - y = 7$,which is always true for any $y$.However,we also know $x + y$ must be a digit. Since $x = y + 7$ and $x \le 9$,the possible values for $y$ are $0, 1, 2$.If $y = 1$,then $x = 8$. The number is $81$.Check: $81 - 63 = 18$,which is the number with interchanged digits. Thus,the number is $81$.

The ten's digit of a two-digit number is greater than the unit's digit by $7$. If we subtract $63$ from the number,the new number obtained is formed by interchanging the digits. Find the number.

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