A single discount equivalent to three successive discounts of 10%, 15% and 18%, is:

Options

A. `35.36% `
B. `34.17% `
C. `37.27% `
D. `32.68% `

Answer

To find a single discount equivalent to three successive discounts of 10%, 15%, and 18%, we can use the formula for successive discounts.

### Step 1: Define the Discounts
Let:
- A = 10%
- B = 15%
- C = 18%

### Step 2: Calculate the First Two Successive Discounts
We will first calculate the equivalent discount for the first two discounts (A and B) using the formula:
\[ \text{Equivalent Discount} = A + B - \frac{A \times B}{100} \]

Substituting the values:
\[ \text{Equivalent Discount} = 10 + 15 - \frac{10 \times 15}{100} \]
\[ = 10 + 15 - \frac{150}{100} \]
\[ = 10 + 15 - 1.5 \]
\[ = 23.5\% \]

### Step 3: Calculate the Final Successive Discount
Now, we will take this equivalent discount (23.5%) and the third discount (C = 18%) to find the overall equivalent discount:
\[ \text{Final Equivalent Discount} = 23.5 + 18 - \frac{23.5 \times 18}{100} \]

Substituting the values:
\[ = 23.5 + 18 - \frac{23.5 \times 18}{100} \]
Calculating \(23.5 \times 18\):
\[ = 423 \]
Now substituting back:
\[ = 23.5 + 18 - \frac{423}{100} \]
\[ = 41.5 - 4.23 \]
\[ = 37.27\% \]

### Conclusion
The single discount equivalent to the three successive discounts of 10%, 15%, and 18% is **37.27%**.

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