Question

the sum of digit of a two digit number is 13 the number obtained by interchanging the digit is 9 more than the original number find the original number .

Answer 1

Hi,  Fresh very goodmorning to you, hope this will help u

Let the unit digit be x

∴ tens digit will be digit becomes [13-x]

∴ the nos is { 10×[13-x] +x}

∴the nos is { 130 -10x+x}

∴the original nos is  [130-9x]

now the number are interchanged

tens digit becomes x

and unit digit becomes [13-x]

now the new number obtained by interchanged are { 10×x+[13-x]}

⇒{ 10x+13-x}

⇒{ 9x+13}

ATP

the number obtained by interchanging the digit is 9 more than the original number

⇒[9x+13]-[130-9x] =9

⇒9x+13-130+9x=9

⇒9x+9x+13-130=9

⇒18x-117=9

⇒18x=9+117 = 126

⇒18x=9+117 = 126

⇒x= 126/18 =7

⇒x=7 ........ [unit digit]

∴tens digit = [13-x]=[13-7] = 6

∴ the nos is 67 ANS

check

⇒76-67=9

⇒6+7=13

Answer 2

Hope this will help you