To solve the problem step by step, let's break it down clearly.
### Step 1: Calculate the first part of the price
The total price of the article is Rs 40,000. The retailer allows a 10% discount on the first 62.5% of the price.
First, we need to find 62.5% of Rs 40,000:
\[
\text{First part} = 62.5\% \text{ of } 40,000 = \frac{62.5}{100} \times 40,000 = 25,000
\]
### Step 2: Calculate the discount on the first part
Now, let's calculate the discount on this first part:
\[
\text{Discount on first part} = 10\% \text{ of } 25,000 = \frac{10}{100} \times 25,000 = 2,500
\]
### Step 3: Calculate the price after the first discount
Now, we will calculate the price after applying the first discount:
\[
\text{Price after first discount} = 25,000 - 2,500 = 22,500
\]
### Step 4: Calculate the remaining price
Next, we need to calculate the remaining amount of the article price after the first part:
\[
\text{Remaining amount} = 40,000 - 25,000 = 15,000
\]
### Step 5: Calculate the discount on the remaining amount
The retailer gives a 4% discount on the remaining amount:
\[
\text{Discount on remaining amount} = 4\% \text{ of } 15,000 = \frac{4}{100} \times 15,000 = 600
\]
### Step 6: Calculate the final price after both discounts
Now, we will calculate the final price after applying both discounts:
\[
\text{Final price} = \text{Price after first discount} + \text{Remaining amount} - \text{Discount on remaining amount}
\]
\[
\text{Final price} = 22,500 + 15,000 - 600 = 36,900
\]
### Step 7: Calculate the overall discount
Now, we can calculate the overall discount given on the article:
\[
\text{Total discount} = \text{Original price} - \text{Final price} = 40,000 - 36,900 = 3,100
\]
### Step 8: Calculate the overall percentage discount
Finally, we calculate the overall percentage discount:
\[
\text{Overall percentage discount} = \left( \frac{\text{Total discount}}{\text{Original price}} \right) \times 100 = \left( \frac{3,100}{40,000} \right) \times 100 = 7.75\%
\]
Thus, the overall percentage discount given on the article is **7.75%**.
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