Question

The sum of the digits of a two digit number is 12. If 18 is added to it ,the digits are reversed. Find the number.​

Answer 1

GIVEN :

• the sum of the digits of a two digit number is 12 .
• If 18 is added to it ,the digit are reversed .

TO FIND :

• find the number

SOLUTION :

Let,

• The Ones digit be 'x'
• The number be '12x - x'

According to the question,

Solving,

$:\implies\sf \:10 x (12 - x) + x \times 1$

$:\implies\sf \: 120 - 10x + x$

$:\implies\sf \:120 - 9x$

Reversed number,

$:\implies\sf \:10 × x + (12-x) x 1$

$:\implies\sf \:10x + 12 - x$

$:\implies\sf \: 9x + 12$

now let,

• digit at tens place be x
• digits at ones place be 12 - x

When 18 is added to the number, its digits are interchanged,

$:\implies\sf \:120 - 9x + 18 = 9x + 12$

$:\implies\sf \:138 - 9x = 9x + 12$

$:\implies\sf \:9x - 9x = 12-138$

$:\implies\sf \:-18x = -126$

$:\implies\sf \:x = 7$

number formed

• 120 - 9x = 120-63 = 57
• 12 + 9x = 12 + 63 = 75

The number is 57

Answer 2

Answer:

Step-by-step explanation:

Let the one's place = x

The ten's place = 12 -x

The number = 10*(12-x) +1* x = 10*12 -10*x  + x

                   = 120 - 10x + x

                   = 120 - 9x

Reversed number = 10*x + 1*(12-x)

                             = 10x + 12 - x

                              =  9x +12

The number + 18 = reversed number

             120 - 9x + 18 = 9x + 12

                   138 - 9x  = 9x +12

             138 - 12 - 9x = 9x

                     126 -9x = 9x

                       126     = 9x + 9x

                           126 = 18x

                           18x = 126

x = 126/18

x = 7

The ten's place = 12 -x = 12 - 7 = 5

Then number = 57