Question

The sum of a 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 tens be x
let the digit in units be y
so the original number is 10x+y
the numbet reversed is 10y+x
the sum is    10x+y+10y+x=165
                     11x+11y=165
                     divide by 11
                      x+y=15
                      x-y=3
                     y=6
                     x=9
so the number is 96

hope this helps u
mark it as brainliest

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

★Unit digit be p

★Ten's digit be c

★Situation :-

10c + p + 10p + c = 165

11p + 11c = 165

★Take common we get :-

11(p + c) = 165

$\tt{\rightarrow p+c=\dfrac{165}{11}}$

p + c = 15 ...... (1)

★Also

p - c = 3 ....... (2)

Or,

c - p = 3 ........ (3)

★Second Situation

c = p - 3 or c = p + 3

★From Equation (1) we have

p + p - 3 = 15 or p + p + 3 = 15

2p = 15 + 3 or 2p = 15 - 3

2p = 18 or 2p = 12

$\tt{\rightarrow p=\dfrac{18}{2}\;or\;p=\dfrac{12}{2}}$

p = 9 or p = 6

$\fbox{Substitute\;1st\;in\;(2)}$

9 - c = 3

9 - 3 = c

6 = c

$\fbox{Now\;second\;value\;in\;(3)}$

c - 6 = 3

c = 3 + 6

c = 9

$\Large{\fbox{Number\;is\;69\;or\;96}}$