Question

the sum of two digit number and the number obtained by reversing the order of is 165 digit differ by 3 find the number

Answer 1

let the no is 10x+y
on reversing no become 10y+x
sum of no's
(10x+y)+(10y+x)=165
11x+11y=165
x+y=15
differ
x-y=3
x+y=15
x-y=3
x=9
y=6
no is 96

Answer 2

Let xy be the two - digit number.

Let the unit's digit be x.

Let the ten's digit be y.

Therefore the decimal expansion is (10x + y).   --------------- (1)

The reverse number will be (10y + x). 

Given that sum of two digit number and number obtained by reversing = 165.

(10x + y) + (10y + x) = 165

10x + y + 10y + x = 165

11x + 11y = 165

x + y = 15   ------------------- (2)


Given that the number differs by 3.

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


On solving (2) & (3), we get

x + y = 15

x - y = 3

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

2x = 18

x = 9

Substitute x = 9 in (3), we get

x - y = 3

9 - y = 3

-y = 3 - 9

-y = - 6

y = 6.

On substituting x & y in (1), we get

10x + y = 10(9) + 6

            = 90 + 6

           = 96.


Therefore the number = 96.


Hope this helps!