Question

The sum of the disit a 2-disit Number is8.the Number obtained by inter changing the disits. Exceeds the given number by 18.find the given number?

Answer 1

let, the unit place digit be a and tens place be b. as it is given b+a=8 original number =10b+a . new number by interchanging the digit= 10a+b . then,( 10a+b)- (10b+a ) =18 》10a+b-10b-a=18 》 9a-9b=18 》 9 (a-b)=18 》 a-b=2 by substitutional method a-b =2 a-b =2 a+b =8 -a-b =-8 -2b=-6 》b=3 so ,from the question a+b=8 , a+3=8 ,a=5. then, the original number = 10b+a = 10× 3+5 =35.