It can be written:
xy = 10x+y ; yx = 10y+x.

Also given,

10y+x = 2(10x+y) - x
=> 4y = 9x
x: y = 4:9
So, x+y will be a multiple of 13. Hence, E.

We use the concept that the number 46, for example, can be expressed as (4)(10) + (6)(1) = 46. Thus, we see that the number “xy” = (10)(x) + (y)(1) = 10x + y.

Since the number “xy” = 10x + y, then its reverse “yx” = 10y + x.

Since “yx” is x less than twice “xy”:

2(10x + y) - x = 10y + x

20x + 2y - x = 10y + x

19x + 2y = 10y + x

18x - 8y = 0

9x - 4y = 0

Since x and y are single digits, the only way 9x - 4y = 0 is if x = 4 and y = 9. Thus, x + y = 4 + 9 = 13.

Answer: E
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