The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number when increased by 9 equals three times the original number. Find the number.

Correct option is A

Given:

Sum of digit of two digit number = 9

Solution:

Let unit digit number = x

Let ten digit number = y

Original number = 10y+x

After interchanging the digit the number = 10x +y

According to question 

x+y = 9

Second condition 

10x +y +9= 3(10y+x)

10x +y+9 =30y +3x

7x +9 = 29y

Put the value of 9 = x+y

7x +x+y =29y

8x =28y

​$$\frac{x}{y}= \frac{7}{2}$$ 

So, value of x= 7 and value of y =2 and the number is27 .