90 = 10 x 9

Clearly, 653xy is divisible by 10, so y = 0

Now, 653x0 is divisible by 9.

So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.

Hence, (x + y) = (4 + 0) = 4.

Unit digit in 7¹⁰⁵ = Unit digit in [ (7⁴)²⁶ x 7 ]

But, unit digit in (7⁴)²⁶ = 1

Unit digit in 7¹⁰⁵ = (1 x 7) = 7

(4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) = 4⁶¹ x (1 + 4 + 4² + 4³) = 4⁶¹ x 85

     = 4⁶⁰ x (4 x 85)

     = (4⁶⁰ x 340), which is divisible by 10.