An article is listed at Rs. 65. A customer bought this article for Rs 56.16 and got two successive discounts of which one is 10%. Find the other discount of this discount scheme that was allowed by the shopkeeper

Answer

To solve the problem step by step, let's break it down:

### Step 1: Identify the Mark Price and the Selling Price
- The mark price (listed price) of the article is Rs. 65.
- The selling price after discounts is Rs. 56.16.

### Step 2: Calculate the First Discount
- The first discount given is 10%.
- To find the amount of the first discount, we calculate 10% of Rs. 65.

\[ \text{First Discount} = 10\% \text{ of } 65 = \frac{10}{100} \times 65 = 6.5 \]

### Step 3: Calculate the Selling Price after the First Discount
- Subtract the first discount from the mark price to find the selling price after the first discount (SP1).

\[ \text{SP1} = \text{Mark Price} - \text{First Discount} = 65 - 6.5 = 58.5 \]

### Step 4: Determine the Second Selling Price
- The selling price after the second discount (SP2) is given as Rs. 56.16.

### Step 5: Calculate the Second Discount
- The second discount can be found by subtracting the final selling price (SP2) from the selling price after the first discount (SP1).

\[ \text{Second Discount} = \text{SP1} - \text{SP2} = 58.5 - 56.16 = 2.34 \]

### Step 6: Calculate the Percentage of the Second Discount
- To find the percentage of the second discount, we use the selling price after the first discount (SP1) as the base.

\[ \text{Percentage of Second Discount} = \left( \frac{\text{Second Discount}}{\text{SP1}} \right) \times 100 = \left( \frac{2.34}{58.5} \right) \times 100 \]

Calculating this gives:

\[ \text{Percentage of Second Discount} = \left( \frac{2.34}{58.5} \right) \times 100 \approx 4\% \]

### Final Answer
The other discount allowed by the shopkeeper is **4%**.

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