Incomplete records – inventory

A sole trader fixes her prices by adding 50% to the cost of all goods purchased. On 31 October 20×3 a fire destroyed a considerable part of inventory and all inventory records

Her trading account for year ended 31 October 20×3 included the following figures:

Sales 281,250
Opening inventory at cost 183,600
Purchases 249,200
432,800
Closing inventory at cost (204,600)
(228,200)
Gross profit 53,050

Using this information, what inventory loss has occurred?

I got the correct answer as per the kit which is 40,700 but i just want to know if i am correct with the way i found the answer the book has it different. I did this

Cost – 100%
Profit – 50%
Sales-150% 281,250/150 x 100 = 187,500

then i subtracted the 187,500 from 228,200 and got 40,700 . I remembered in your lecture you said higher closing inventory less cost of sale and vice versa. So if cost suppose to be 187,500 then that extra 40,700 has to be the inventory lost am i correct?