Question

the sum of a two digit number and the no obtained by reversing the digits is 66.if the digits differ by 2.find the number​

Answer 1

Step-by-step explanation:

Let the original number be =10x+y

Reversed no.=10y+x

ATQ:

10x+y+10y+x=66

11x+11y=66

11(x+y)=66

x+y=6..............(1)

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

Therefore by adding the equation

2x=8

x=4

Therefore y=2

Original number=10x+y

=10*4+2

=42

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Questions}}}}$

Assume

Unit digit be v and n respectively

So,

Situation

10n + v + 10v + n = 66

11n + 11v = 66

11(v + n) = 66

$\rm \: \: \: \: \: \: \: \: \:(v+n)=\dfrac{\cancel{66}}{\cancel{11}}$

v + n = 6 ........ (1)

Also,

v - n = 2 ......... (2)

$\Large{\boxed{\bigstar{{Adding\;both\;Equation :-}}}}$

2v = 8

$\rm \: \: \: \: \: \: \: \: \:v=\dfrac{\cancel{8}}{\cancel{2}}$

v = 4

Now,

4 + n = 6

n = 6 - 4

n = 2

Hence,

$\huge{\boxed{\sf\:{Number = 24\;or\;42}}}$