Question

1. The sum of the digits of a two-digit number is 8. If the digits are reversed, the new number
increases by 18. Find the number.

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Answer 1

Step-by-step explanation:

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.

Answer 2

Step-by-step explanation:

the numbers are 53 and 35