Three successive discounts of 10%, 12% and 15% amount to a single discount of:

Options

A. 0.3628
B. 0.3468
C. 0.37
D. None of these

Answer

To find the single equivalent discount for three successive discounts of 10%, 12%, and 15%, we can use the formula for calculating the equivalent discount for two successive discounts, which is given by:

\[ \text{Equivalent Discount} = a + b - \frac{a \times b}{100} \]

### Step 1: Calculate the equivalent discount for the first two discounts (10% and 12%).

Let \( a = 10\% \) and \( b = 12\% \).

Using the formula:

\[ \text{Equivalent Discount} = 10 + 12 - \frac{10 \times 12}{100} \]

Calculating \( \frac{10 \times 12}{100} \):

\[ \frac{10 \times 12}{100} = \frac{120}{100} = 1.2 \]

Now substituting back into the equation:

\[ \text{Equivalent Discount} = 10 + 12 - 1.2 = 22 - 1.2 = 20.8\% \]

### Step 2: Now calculate the equivalent discount of the result from Step 1 (20.8%) and the third discount (15%).

Let \( a = 20.8\% \) and \( b = 15\% \).

Using the formula again:

\[ \text{Equivalent Discount} = 20.8 + 15 - \frac{20.8 \times 15}{100} \]

Calculating \( \frac{20.8 \times 15}{100} \):

\[ \frac{20.8 \times 15}{100} = \frac{312}{100} = 3.12 \]

Now substituting back into the equation:

\[ \text{Equivalent Discount} = 20.8 + 15 - 3.12 = 35.8 - 3.12 = 32.68\% \]

### Final Result

The single equivalent discount for the three successive discounts of 10%, 12%, and 15% is **32.68%**.

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