Question

.The sum of the two digits number is 8.the number obtained by interchanging the digits exceeds original number by 18,so what is the original number (descriptive)

Answer 1

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• The sum of the two digits number is 8.

• The number obtained by interchanging the digits exceeds original number by 18.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The original number.

$\bf\underline{\underline{\green{Solution:-}}}$

$\sf Let\: the \: tens\: digit\: of \: the \: number \: be \: x$

$\sf And, \: the \: units\: digit\: of \: the \: number \: be \: y$

$\sf The\: original \: number = 10x + y$

$\sf The\: number \: obtained \: by \: interchanging \: the \: digits = 10y + x$

$\bf\underline{\pink{Case\: 1:-}}$

The sum of the two digits number is 8.

$\sf \implies x + y = 8..…..(i)$

$\bf\underline{\orange{Case\: 2:-}}$

The number obtained by interchanging the digits exceeds original number by 18.

$\sf Reversed\: number - Original\: number = 18$

$\sf \implies 10y + x - (10x + y) = 18$

$\sf \implies 10y + x - 10x - y = 18$

$\sf \implies 9y - 9x = 18$

$\sf Divide\: the \: equation \: by \: 9$

$\sf \implies y - x = 2......(ii)$

$\underline{\sf Adding \: equations\: (i) \: and \: (ii)}$

$\sf \implies x + y + y - x = 2 + 8$

$\sf \implies 2y = 10$

$\sf \implies y = 5$

$\underline{\sf Substituting\: y = 5\: in \: equation\: (i)}$

$\sf \implies x + y = 8$

$\sf \implies x + 5 = 8$

$\sf \implies x = 8 - 5$

$\sf \implies x = 3$

$\sf The \: original \: number = 10x + y$

$\sf = 10(3) + 5$

$\sf = 30 + 5$

$\sf = 35$

$\large\underline{\boxed{\purple{\rm \therefore The \: original \: number = 35}}}$