If x and y are the two digits of the number 115 xy such that this number is divisible by 90, then the value of x + y is:

Correct option is B

Given:

The number is 115xy , where x and y are digits.
The number is divisible by 90 .
For a number to be divisible by 90 , it must be divisible by both 9 and 10 .

Solution:
Step 1: Check divisibility by 10

A number is divisible by 10 if its last digit is 0 .
Thus, y = 0 .
Step 2: Check divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9 .
The number 115xy has digits 1, 1, 5, x, and y .
Substitute y = 0 :
Sum of digits = 1 + 1 + 5 + x + 0 = 7 + x

For divisibility by 9 :
7 + x must be divisible by 9.
The smallest value of x that satisfies this condition is x = 2 , since:
7 + 2 = 9, which is divisible by 9.
Step 3: Find x + y

Substitute x = 2 and y = 0 :
x + y = 2 + 0 = 2

The value of x + y is 2 .