I did it this way -

Utility without lottery = 10 (100)^1/2 = 100

Expected value of lottery = 400p+49(1-p) = 351p+49

Utility of expected value of lottery =10(351p+49)^1/2

Equating this to 100 for indifference, we get p = 51/351

But the answer is p>51/221 and not 51/351 !

I also tried another way

I found Utility of the lottery = p U(winning)+(1-p) U(losing) = p 10(400)^1/2 + (1-p) 10(49)^1/2 = 130p+70

Equating to 100 for indifference, p = 3/13

This p is equal to the answer given

How is this happening??