Find a single discount equivalent to three successive discounts of 20%, 10% and 5% ?

Answer

To find a single discount equivalent to three successive discounts of 20%, 10%, and 5%, we can follow these steps:

### Step 1: Understand the Formula
When you have two successive discounts of \( a\% \) and \( b\% \), the equivalent single discount can be calculated using the formula:
\[ \text{Single Discount} = a + b - \frac{a \times b}{100} \]

### Step 2: Calculate the First Two Discounts
Let's first calculate the single discount for the first two discounts: 20% and 10%.

Let \( a = 20 \) and \( b = 10 \).

Using the formula:
\[ \text{Single Discount} = 20 + 10 - \frac{20 \times 10}{100} \]
Calculating the multiplication:
\[ 20 \times 10 = 200 \]
Now, divide by 100:
\[ \frac{200}{100} = 2 \]
Now substitute this back into the equation:
\[ \text{Single Discount} = 20 + 10 - 2 = 28\% \]

### Step 3: Calculate the Final Discount with the Third Discount
Now, we will use the result from the first two discounts (28%) and the third discount (5%).

Let \( a = 28 \) and \( b = 5 \).

Using the formula again:
\[ \text{Single Discount} = 28 + 5 - \frac{28 \times 5}{100} \]
Calculating the multiplication:
\[ 28 \times 5 = 140 \]
Now, divide by 100:
\[ \frac{140}{100} = 1.4 \]
Now substitute this back into the equation:
\[ \text{Single Discount} = 28 + 5 - 1.4 = 31.6\% \]

### Final Answer
The single discount equivalent to three successive discounts of 20%, 10%, and 5% is **31.6%**.

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