Question

11. 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

Answer:

57

Step-by-step explanation:

Let the unit digit be x,

and, tens digit be y

According to the question,

x + y = 12. .....................(1)

The real number is x + 10y

And the reversed number is 10x + y

Now,

x + 10y + 18 = 10x + y

10y - y + 18 = 10x -x

9y + 18 = 9x

18 = 9x - 9y

9x - 9y = 18

9( x - y ) = 18

x - y = 18/9

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

Add in equation (1) and (2).

x + y + x - y = 12 + 2

2x = 14

x = 14/2

x = 7

put the value of ‘x’ in equation (2)

7 - y = 2

-y = 2 - 7.

y = 5

Hence, the obtained number is:-

x + 10y

= 7 + 10 × 5

= 57

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