The single discount equivalent to three successive discounts of `20%` `15%, 10%` is

Options

A. `50. 3%`
B. `38.8%`
C. `40.32%`
D. `45%`

Answer

To find the single discount equivalent to three successive discounts of 20%, 15%, and 10%, we can use the formula for successive discounts. The formula is:

\[ \text{Single Discount} = A + B - \frac{AB}{100} \]

where A and B are the successive discounts.

### Step 1: Calculate the first two discounts (20% and 15%)

Let:
- A = 20%
- B = 15%

Using the formula:

\[ \text{Single Discount} = A + B - \frac{AB}{100} \]

Substituting the values:

\[ \text{Single Discount} = 20 + 15 - \frac{20 \times 15}{100} \]

Calculating \( \frac{20 \times 15}{100} \):

\[ \frac{300}{100} = 3 \]

Now substituting back:

\[ \text{Single Discount} = 20 + 15 - 3 = 32% \]

### Step 2: Now calculate the discount with the third discount (10%)

Now we have the effective discount after the first two discounts as 32%. We will now consider this as A and the third discount (10%) as B.

Let:
- A = 32%
- B = 10%

Using the formula again:

\[ \text{Single Discount} = A + B - \frac{AB}{100} \]

Substituting the values:

\[ \text{Single Discount} = 32 + 10 - \frac{32 \times 10}{100} \]

Calculating \( \frac{32 \times 10}{100} \):

\[ \frac{320}{100} = 3.2 \]

Now substituting back:

\[ \text{Single Discount} = 32 + 10 - 3.2 = 38.8% \]

### Final Answer

The single discount equivalent to three successive discounts of 20%, 15%, and 10% is **38.8%**.

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