Let F = number of fans she should purchase.

And B = number of bicycles.

F +B = 40 -----------------------(1)

360(F) +2360(B) = 55,400 ---------(2)

From (1), F = 40 -B

Substitute that into (2),

360(40 -B) +2360(B) = 55,400

14,400 -360(B) +2360(B) = 55,400

2000(B) = 55,400 -14,400

2000(B) = 41,000

B = 41,000/2000 = 20.5 bicycles.

Or, B = 20 bicycles

So, F = 40 -20 = 20 fans

Check,

20(360) +2360(20) = 54,400 ----------ok.

Therefore, she should purchase 20 each of the fans and the bicycles.

Profit = 50(20) +500(20) = 11,000 Rs.

In percentage,

11,000 / 54,400 = 0.2022 -----that is 20.22% profit.