Question

The sum of two digits number obtained on reversing the digit is 165, and the digits differ by 3. Frame two equations and solve them by cross method to find the two digit number.

Answer 1

let first digit be x and second be y therefore the no will be 10x+y
no we will get on reversing the digit is 10y+x
therefore equation will be.
10x+y+10y+x=165
so x+y=15
as given difference is 3 therefore equation will be x-y=3
by eliminating y we will get equation 2x=12
so x=6 and y=9

Answer 2

let unit's digit be x
then tens digit be x-3
no.=10(x-3)+x
reverse no.=10x+x-3
according to question,
10x-30+x+10x+x-3=165
22x-33=165
22x=165+33
22x=198
x=198/22
x=9
x-3=9-3=6
so the number =69 or 96