A shopkeeper offers the following three schemes. Which scheme has the lowest discount percentage (all articles have same marked price) ?
I. Two successive discounts of 10% and 10%
II. Buy 7 get 8
III. Buy 9 get 1 free

Options

A. Only II
B. Only III
C. Only II and III
D. All are equal

Answer

To determine which scheme has the lowest discount percentage, we will analyze each of the three schemes step by step.

### Step 1: Calculate the effective discount for Scheme I (Two successive discounts of 10% and 10%)

1. **First Discount**: Let's assume the marked price of an article is \( P \).
- After the first discount of 10%, the price becomes:
\[ P - 0.10P = 0.90P \]

2. **Second Discount**: Now, applying the second discount of 10% on the new price:
- The price after the second discount is:
\[ 0.90P - 0.10(0.90P) = 0.90P - 0.09P = 0.81P \]

3. **Total Discount**: The total discount given is:
\[ P - 0.81P = 0.19P \]
- The discount percentage is:
\[ \frac{0.19P}{P} \times 100 = 19\% \]