31. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & dr = 15\% = 0.15 \\ & sp = \text{₱680}\end{aligned}[/tex]Step 2: Solve for the original price.[tex]\begin{aligned} op & = \frac{sp}{1 - dr} \\ & = \frac{680}{1 - 0.15} \\ & = \boxed{\text{₱800}} \end{aligned}[/tex]Hence, the price of an article is ₱800.32. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & dr = 10\% = 0.1 \\ & op = \text{₱1,650}\end{aligned}[/tex]Step 2: Solve for the discount and the selling price.(i) Discount:[tex]\begin{aligned} d & = (op)(dr) \\ & = (1,650)(0.1) \\ & = \boxed{\text{₱165}} \end{aligned}[/tex]Hence, the discount given is ₱165.(ii) Selling Price:[tex]\begin{aligned} sp & = op - d \\ & = 1,650 - 165 \\ & = \boxed{\text{₱1,485}} \end{aligned}[/tex]Hence, the selling price of the book is ₱1,485.