Three successive discounts of 15%, 10% and 8% is equivalent to a single discount of:

Options

A. `30.52%`
B. `28.22%`
C. `29.62%`
D. `30.62%`

Answer

To find the equivalent single discount of three successive discounts of 15%, 10%, and 8%, 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 (15% and 10%)

Let \(A = 15\%\) and \(B = 10\%\).

Using the formula:

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

Substituting the values:

\[ \text{Single Discount} = 15 + 10 - \frac{15 \times 10}{100} \]

Calculating:

\[ = 25 - \frac{150}{100} \]
\[ = 25 - 1.5 \]
\[ = 23.5\% \]

### Step 2: Now include the third discount (8%)

Now, we will use the result from Step 1 (23.5%) as the new \(A\) and the third discount \(B = 8\%\).

Using the formula again:

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

Substituting the values:

\[ \text{Single Discount} = 23.5 + 8 - \frac{23.5 \times 8}{100} \]

Calculating:

\[ = 31.5 - \frac{188}{100} \]
\[ = 31.5 - 1.88 \]
\[ = 29.62\% \]

### Final Answer

The equivalent single discount of three successive discounts of 15%, 10%, and 8% is **29.62%**.

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