41, 12

x-2y = 17

x+y = 53

y>x

Let the two numbers be L and S.

The sum of the two numbers is 53

L + S = 53 ...(1)

Twice the smaller number subtracted from the larger number gives 17.

L - 2S = 17 ...(2)

(1) - (2)

=> L + S - L + 2S = 53 - 17

=> 3S = 36

=> S = 12

L = 53 - S = 53 - 12 = 41

**The smaller number is 12 and the larger number is 41.**