If 764xy is divisible by 90, then what will be the value of x+y?

Given that the number 764xy is divisible by 90

If a number is divisible by 90 then it should be divisible by both 9 and 10.

(Because 90 can be written as a product of two co-prime numbers as 9 × 10. So, the divisibility rule of 90 is that if a number is divisible by both 9 and 10then it will also be divisible by 90. As the given number is said to be divisible by 90, we can definitely say that it is divisible by both 9 and 10.)

For a number to be divisible by 10, its unit digit should be 0

For a number to be divisible by 10, its unit digit should be 0

So, in the given number 764xy the unit digit y should be = 0

For a number to be divisible by 9, its digital sum should be a multiple of 9

Digital sum known so far = (7 + 6 + 4 + x + 0) = (17 + x)

To make this digital sum a multiple of 9, let us consider a multiple of 9 that is close to 17.

One such multiple of 9 is 18.

To get the digital sum as 18, the value of x should be = 1

(If (17 + x) = 18, then x = (18 - 17) = 1) Thus, we found the value of x = 1 and y = 0 So, the required value of (x + y) = (1 + 0) = 1