Sum of the digits of a 2-digit number is 9. On reversing its digits, t

1.	Sum of the digits of a 2-digit number is 9. On reversing its digits, the new number obtained is 45 re than the original number. Find the number
Answer» align="absmiddle" alt="\sf\large\underline\purple{LET:-}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Csf%5Clarge%5Cunderline%5Cpurple%7BLet%3A-%7D" title="\sf\large\underline\purple{Let:-}"> $\tt{\implies The\: ones\:digit\:be\:x}$ $\tt{\implies The\:tens\:digit\:be\:y}$ $\tt{\implies The\: orginal\: <klux>NUMBER</klux>=10y+x}$ $\tt{\implies The\: reversed\: number=10x+y}$ $\sf\large\underline\purple{To\: <klux>FIND</klux>:-}$ $\tt{\implies The\: orginal\: number=?}$ $\sf\large\underline\purple{Solution:-}$ To calculate the original number at first we have to set up equation with the help of given clue in the question. Then calculate the value of x and y after that find out the original number:-] $\sf\small\underline\red{Given\:in\:case\:(i):-}$ $\tt{\implies sum\:of\:2\: digits=9}$ $\tt{\implies x+y=9----(i)}$ $\sf\small\underline\red{Given\:in\:case\:(i):-}$ $\tt{\implies orginal\: number+45=reversed\: number}$ $\tt{\implies 10y+x+45=10x+y}$ $\tt{\implies 10x-x+y-10y=45}$ $\tt{\implies 9x-9y=45}$ Here DIVIDING by 9 on both sides:-] $\tt{\implies x-y=5----(ii)}$ In eq (i) and (ii) SOLVING by adding:-} $\tt{\implies x+y=9}$ $\tt{\implies x-y=5}$ By solving we get here:-] $\tt{\implies 2x=14}$ $\tt{\implies x=7}$ In eq (i) putting the value of x=7:-] $\tt{\implies x+y=9}$ $\tt{\implies x+7=9}$ $\tt{\implies x=9-7}$ $\tt{\implies x=2}$ $\sf\large{Hence,}$ $\tt{\implies Orginal\: number=10y+x}$ $\tt{\implies Orginal\: number=10*7+2}$ $\tt{\implies Orginal\: number=70+2}$ $\tt{\implies Orginal\: number=72}$

Sum of the digits of a 2-digit number is 9. On reversing its digits, the new number obtained is 45 re than the original number. Find the number

Answer»

align="absmiddle" alt="\sf\large\underline\purple{LET:-}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Csf%5Clarge%5Cunderline%5Cpurple%7BLet%3A-%7D" title="\sf\large\underline\purple{Let:-}">

$\tt{\implies The\: ones\:digit\:be\:x}$

$\tt{\implies The\:tens\:digit\:be\:y}$

$\tt{\implies The\: orginal\: <klux>NUMBER</klux>=10y+x}$

$\tt{\implies The\: reversed\: number=10x+y}$

$\sf\large\underline\purple{To\: <klux>FIND</klux>:-}$

$\tt{\implies The\: orginal\: number=?}$

$\sf\large\underline\purple{Solution:-}$

To calculate the original number at first we have to set up equation with the help of given clue in the question. Then calculate the value of x and y after that find out the original number:-]

$\sf\small\underline\red{Given\:in\:case\:(i):-}$