Question

The sum of the digits of a two-digit number is 8. The number obtained by interchanging its digits is 18 more than the original number. Find the original number Let the tens and units digits of the required number hea and h respectively. Then,​

Answer 1

Let x be the digit at unit’s place and y be the digit at ten’s place.

Since y is at ten’s place, then the number formed is 10y+x.

By reversing the digits, it becomes 10x+y.

As the difference of the numbers is 18, so,

(10y+x)−(10x+y)=18

9(y−x)=18

y−x=2 .... (1)

As the sum of digits is 8, so,

x+y=8 .... (2)

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

2y=10⇒y=5

Putting this in (2), we get x=8−5=3

x=3,y=5

Hence, number =10y+x=10×5+3=53.