Question

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

Please answer with good explanation!

Answer 1

You meant “the digits are reversed; what is the original number?” 

The solution can be obtained by letting x be the ‘tens digit’, and y be the unit digit, so that the original number is 10x+y. 

Then 10x+y+18=10y+x, because the digits are reversed. This simplifies to 9x+18=9y, or x+2=y. Since the digits add up to 12, x+y=12. Substituting for y yields x+2=12-x, which simplifies to x=5. Then y=7, so the original number is 57. 57+18 = 75.

Answer 2

Answer:

Let the unit digit be x,

=> and , tens digit be y.

→A/Q

↪➡ 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.

⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴

✴✴ Thanks!!✴✴.

☺☺☺ Hope it is helpful for you ✌✌✌.