Question

The sum of the digits of a 2-digit number is 12. The number obtained by interchanging its digits is 18 more than the original number. Find the original number.

Answer 1

Answer:

Let the tens digit of the required number be x and the units digit be y. Then,

x+y=12  .........(1)

Required Number = (10x+y).

Number obtained on reversing the digits = (10y+x).

Therefore,

(10y+x)−(10x+y)=18

9y−9x=18

y−x=2     ..........(2)

On adding (1) and (2), we get,

2y=14⟹y=7

Therefore, 

x=5

Hence, the required number is 57.

Answer 2

Answer:

Original number =57

Step-by-step explanation:

Let the original number be 10x +y

By the given information

x+y =12

Let the interchanged number be 10y+x

Accordingly

10x +y = 18 + 10y + x

On solving the equation, we get

x = 5 and y =7

Thus the number is 57