The single discount equal to three consecutive discounts of 10%, 12% and 5% is

Options

A. 0.2627
B. 0.2476
C. `9%
D. 0.11

Answer

To find the single discount equivalent to three consecutive discounts of 10%, 12%, and 5%, we can use the formula for calculating the equivalent discount for two successive discounts:

\[ D_{eq} = D_1 + D_2 - \frac{D_1 \times D_2}{100} \]

Where \(D_1\) and \(D_2\) are the two discounts.

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

Let:
- \(D_1 = 10\%\)
- \(D_2 = 12\%\)

Using the formula:

\[ D_{eq1} = 10 + 12 - \frac{10 \times 12}{100} \]

Calculating \(10 + 12\):

\[ D_{eq1} = 22 - \frac{120}{100} \]

Calculating \(\frac{120}{100}\):

\[ D_{eq1} = 22 - 1.2 = 20.8\% \]

### Step 2: Now calculate the equivalent discount using the result from Step 1 (20.8%) and the third discount (5%).

Let:
- \(D_1 = 20.8\%\)
- \(D_2 = 5\%\)

Using the formula again:

\[ D_{eq2} = 20.8 + 5 - \frac{20.8 \times 5}{100} \]

Calculating \(20.8 + 5\):

\[ D_{eq2} = 25.8 - \frac{104}{100} \]

Calculating \(\frac{104}{100}\):

\[ D_{eq2} = 25.8 - 1.04 = 24.76\% \]

### Final Result

The single discount equivalent to three consecutive discounts of 10%, 12%, and 5% is **24.76%**.