Find a single discount (as percent) equivalent to following successive discounts:
`10%, 20% and 20%`

Answer

To find a single discount equivalent to the successive discounts of 10%, 20%, and 20%, we can follow these steps:

### Step 1: Identify the Discounts
Let:
- \( D_1 = 10\% \)
- \( D_2 = 20\% \)
- \( D_3 = 20\% \)

### Step 2: Calculate the First Two Successive Discounts
We will use the formula for combining two successive discounts:
\[ D = D_1 + D_2 - \frac{D_1 \times D_2}{100} \]
Substituting \( D_1 \) and \( D_2 \):
\[ D' = 10 + 20 - \frac{10 \times 20}{100} \]

### Step 3: Simplify the Calculation
Calculate \( \frac{10 \times 20}{100} \):
\[ \frac{10 \times 20}{100} = \frac{200}{100} = 2 \]
Now substitute back into the equation:
\[ D' = 10 + 20 - 2 = 28\% \]

### Step 4: Combine the Result with the Third Discount
Now we will combine \( D' \) with \( D_3 \) using the same formula:
\[ D'' = D' + D_3 - \frac{D' \times D_3}{100} \]
Substituting \( D' = 28\% \) and \( D_3 = 20\% \):
\[ D'' = 28 + 20 - \frac{28 \times 20}{100} \]

### Step 5: Simplify the Calculation Again
Calculate \( \frac{28 \times 20}{100} \):
\[ \frac{28 \times 20}{100} = \frac{560}{100} = 5.6 \]
Now substitute back into the equation:
\[ D'' = 28 + 20 - 5.6 = 48 - 5.6 = 42.4\% \]

### Final Answer
The single discount equivalent to the successive discounts of 10%, 20%, and 20% is:
\[ \boxed{42.4\%} \]