Question

The sum of digits of a 2 digit number By 13 .the number obtained by interchanging its digit exceeds the given numbr by 9.find the number

Answer 1

let the 1st no be x

and let the 2nd no be y

acc to the ques

x+y =13 -------- 1

let the original be 10x+y

on interchanging the digits the no becomes 10y+x

now according to the ques

10y+x=10x+y+9

10y-y+x-10x=9

9y-9x=9

9(y-x)=9

y-x=9/9

y-x=1

-x+y = 1 ---------2

now we solve the equations using elimination method

from eq 1 and 2

x+y=13

+(-x+y=1)

-----------------

0+2y= 14

-----------------

y = 14/2

y= 7

now we can substitute the value of y in eq 1

x+y=13

x+7=13

x=13-7

x=6

hence the number is 67

hope this ans helps u :)