Question

The sum of two digit number and the number obtained by reversing the order of its digits is 165. If the digits differ by 3 , find the number.

Answer 1

let the digit in 10s place be x
     the digit in ones place is y
so,the number is 10x+y and the number obtained by reversing it's digitsis10y+x
sum is 165
so 10x+y+10y+x=165
11x+11y=165
by taking 11 as common multiple we get
x+y=15............eq 1
here it is given that the digits differ by 3
so x-y=3...........eq 2

solving equation 1 and 2
  
                                     x+y=15
                                     x-y=03
subtracting the equations we get
                                   2y=12
                                      y=6
substitute y=6 in equation 1(eq 1)
                                x+6=15
                                x=15-6
                                x=9
so the number is 96

Answer 2

let the units place digit be y

and tens place digit be x

so number will be 10x+y

by reversing the digits the number

became 10y+x

10x+y+10y+x=165

11y+11x=165

x+y=15

digits differ by 3

so there are 2 possibilities

1 ) x>y

so

x-y=3 ....... (2)

2 ) y>x

so

y-x=3 ....... (3)

If we consider equation (1) & (2)

by adding (1) &(2) we get,

2x=18

x=9

If we consider (1) &(3)

by adding (1) &(3) we get,

2y=18

y=9

x=6

the number is either 96 or 69