Take the usual selling price of the puzzle as 100%.
10% discount : 100% - 10% = 90% of the usual selling price.
30% discount : 100% - 30% = 70% of the usual selling price.

Difference between the two discounted prices = 90% - 70% = 20% of the usual selling price.
Difference also = $40 - $10 = $30
So $30 = 20% of the usual selling price
10% of the usual selling price = $30 ÷ 2 = $15
70% of the usual selling price = $15 × 7 = $105
Cost price of puzzle = $105 - $10 = $95
Or
90% of the usual selling price = $15 × 9 = $135
Cost price of puzzle = $135 - $40 = $95

Additional info that can be found:
Usual selling price → 100% → $30 × 5 = $150