Question

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 1

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

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

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

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

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

$\sf\large\underline\purple{To\: Find:-}$

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

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

• 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:-]

$\tt{\implies x+y=9}$

$\tt{\implies x+7=9}$

$\tt{\implies x=9-7}$

$\tt{\implies x=2}$

$\sf\large{Hence,}$

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

$\tt{\implies Orginal\: number=10*7+2}$

$\tt{\implies Orginal\: number=70+2}$

$\tt{\implies Orginal\: number=72}$

Answer 2

Let

the two digits be x and y

sum of 2 digits=9

x+y=9-----1

on reversing it's digits the new number is 45 is more

10y+x+45=10x+y

x-y=5

if we solve this both equation we get,

x=2 y=7

so,

original number=10y+x=10×7+2=72