.The sum of the two digits number is 8.the number obtained by intercha

1.	.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» ong>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. $\sf Reversed\: number - Original\: number = 18$ $\sf \implies 10y + x - (10x + y) = 18$ $\sf \implies 10y + x - 10x - y = 18$ $\sf \implies 9y - 9x = 18$ $\sf Divide\: the \: equation \: by \: 9$ $\sf \implies y - x = 2......(ii)$ $\underline{\sf Adding \: equations\: (i) \: and \: (ii)}$ $\sf \implies x + y + y - x = 2 + 8$ $\sf \implies 2y = 10$ $\sf \implies y = 5$ $\underline{\sf Substituting\: y = 5\: in \: equation\: (i)}$ $\sf \implies x + y = 8$ $\sf \implies x + 5 = 8$ $\sf \implies x = 8 - 5$ $\sf \implies x = 3$ $\sf The \: original \: number = 10x + y$ $\sf = 10(3) + 5$ $\sf = 30 + 5$ $\sf = 35$ $\large\underline{\boxed{\purple{\rm \therefore The \: original \: number = 35}}}$