A retail offers the following discount scheme for buyers on an article.
I. Two successive discounts of 10%.
II. A discount of 12% following by a discount of 8%
III. Successive discounts of 15% and 5%
IV. A discount of 20%
The selling price will be minimum under the scheme.

Answer

To determine which discount scheme results in the minimum selling price, we need to calculate the effective discount for each scheme. We will use the formula for successive discounts, which is given by:

\[ \text{Effective Discount} = x + y + \frac{xy}{100} \]

where \(x\) and \(y\) are the two successive discounts.

### Step 1: Calculate the effective discount for the first scheme (Two successive discounts of 10%)
- Here, \(x = 10\%\) and \(y = 10\%\).

\[ \text{Effective Discount} = 10 + 10 + \frac{10 \times 10}{100} = 20 + 1 = 21\% \]

### Step 2: Calculate the effective discount for the second scheme (A discount of 12% followed by a discount of 8%)
- Here, \(x = 12\%\) and \(y = 8\%\).

\[ \text{Effective Discount} = 12 + 8 + \frac{12 \times 8}{100} = 20 + 0.96 = 20.96\% \]

### Step 3: Calculate the effective discount for the third scheme (Successive discounts of 15% and 5%)
- Here, \(x = 15\%\) and \(y = 5\%\).

\[ \text{Effective Discount} = 15 + 5 + \frac{15 \times 5}{100} = 20 + 0.75 = 20.75\% \]

### Step 4: Calculate the effective discount for the fourth scheme (A discount of 20%)
- Here, there is only one discount, so the effective discount is simply:

\[ \text{Effective Discount} = 20\% \]

### Step 5: Compare all the effective discounts
- Scheme I: 21%
- Scheme II: 20.96%
- Scheme III: 20.75%
- Scheme IV: 20%

### Conclusion
The minimum selling price will be under the first scheme, which offers two successive discounts of 10%, resulting in an effective discount of **21%**.

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