Mohan goes to furniture shop to buy a sofa set and a centre table. He bargains for a 10% discount on the centre table and 25% discount on sofa set. However, the shopkeeper, by mistake, interchanged the discount percentage figures while making the bill and mohit paid accordingly. When compared to what he should pay for his purchases, what percentage did mohit pay extra given that the centre table costs 40% as much as the sofa set.

Options

A. `12.3`%
B. `7.2%`
C. `8.1%`
D. `6.3%`

Answer

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

### Step 1: Define the Cost Prices
Let the cost price (CP) of the sofa set be \( CP_{sofa} = 100 \).
Since the centre table costs 40% as much as the sofa set, we have:
\[ CP_{table} = 40\% \text{ of } CP_{sofa} = 0.4 \times 100 = 40. \]

### Step 2: Calculate the Actual Bill with Correct Discounts
Mohan bargained for a 10% discount on the centre table and a 25% discount on the sofa set.

- **Discount on Centre Table:**
\[ \text{Discount} = 10\% \text{ of } 40 = 0.1 \times 40 = 4. \]
\[ \text{Price after discount} = 40 - 4 = 36. \]

- **Discount on Sofa Set:**
\[ \text{Discount} = 25\% \text{ of } 100 = 0.25 \times 100 = 25. \]
\[ \text{Price after discount} = 100 - 25 = 75. \]

- **Total Actual Bill:**
\[ \text{Total Actual Bill} = 36 + 75 = 111. \]

### Step 3: Calculate the Bill with Interchanged Discounts
The shopkeeper mistakenly interchanged the discount percentages: 10% on the sofa set and 25% on the centre table.

- **Discount on Centre Table (mistakenly applied):**
\[ \text{Discount} = 25\% \text{ of } 40 = 0.25 \times 40 = 10. \]
\[ \text{Price after discount} = 40 - 10 = 30. \]

- **Discount on Sofa Set (mistakenly applied):**
\[ \text{Discount} = 10\% \text{ of } 100 = 0.1 \times 100 = 10. \]
\[ \text{Price after discount} = 100 - 10 = 90. \]

- **Total Bill with Mistaken Discounts:**
\[ \text{Total Mistaken Bill} = 30 + 90 = 120. \]

### Step 4: Calculate the Extra Amount Paid
Now we find the extra amount Mohan paid compared to what he should have paid:
\[ \text{Extra Amount Paid} = \text{Total Mistaken Bill} - \text{Total Actual Bill} = 120 - 111 = 9. \]

### Step 5: Calculate the Percentage Extra Paid
To find the percentage of extra amount paid:
\[ \text{Percentage Extra Paid} = \left( \frac{\text{Extra Amount Paid}}{\text{Total Actual Bill}} \right) \times 100 = \left( \frac{9}{111} \right) \times 100. \]
Calculating this gives:
\[ \text{Percentage Extra Paid} \approx 8.1\%. \]

### Final Answer
Mohan paid approximately **8.1% extra**.

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