A series of successive discounts of 20%, 10%, and 5% is equivalent to what single discount?

Step 1: Convert into multipliers
20% discount → $0.80$
10% discount → $0.90$
5% discount → $0.95$

Step 2: Multiply

$0.80 \times 0.90 \times 0.95$

$= 0.72 \times 0.95 = 0.684$

Step 3: Find total discount

Equivalent price factor = $0.684$

So discount = $1 - 0.684 = 0.316$

Step 4: Convert to percentage

$0.316 = 31.6%$

Final Answer: 31.6%