Three consecutive discounts of 22%, 17% and 11 % are equivalent to a single discount of _____.

Options

A. Approx 50%
B. Approx 42%
C. Approx 25%
D. Approx 45%

Answer

To find the equivalent single discount of three consecutive discounts of 22%, 17%, and 11%, we can use the formula for successive discounts. The formula for two successive discounts A and B is given by:

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

**Step 1: Calculate the first two discounts (22% and 17%)**

Let A = 22% and B = 17%.

Using the formula:

\[ \text{Single Discount} = 22 + 17 - \frac{22 \times 17}{100} \]

Calculating the product:

\[ 22 \times 17 = 374 \]

Now substituting back into the formula:

\[ \text{Single Discount} = 22 + 17 - \frac{374}{100} \]

Calculating \(\frac{374}{100} = 3.74\):

\[ \text{Single Discount} = 39 - 3.74 = 35.26\% \]

**Step 2: Now calculate the discount with the third discount (11%)**

Now we will take the result from Step 1 (35.26%) as A and the third discount (11%) as B.

Let A = 35.26% and B = 11%.

Using the formula again:

\[ \text{Single Discount} = 35.26 + 11 - \frac{35.26 \times 11}{100} \]

Calculating the product:

\[ 35.26 \times 11 = 387.86 \]

Now substituting back into the formula:

\[ \text{Single Discount} = 35.26 + 11 - \frac{387.86}{100} \]

Calculating \(\frac{387.86}{100} = 3.8786\):

\[ \text{Single Discount} = 46.26 - 3.8786 \approx 42.38\% \]

**Final Answer:**

The equivalent single discount of three consecutive discounts of 22%, 17%, and 11% is approximately **42%**.

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