Tinkawala purchased the articles for ₹ 123684. He sold `60%` of those at a profit of `16.66%` and rest at a loss. Find the loss percentage on the remaining if the overall loss is `14%`?

Options

A. `20%`
B. `30%`
C. `60%`
D. `66.66%`

Answer

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

### Step 1: Calculate the total cost price
Tinkawala purchased the articles for ₹123684.

### Step 2: Determine the quantity sold at profit
Tinkawala sold 60% of the articles. Therefore, the cost price of the articles sold at profit is:
\[ \text{Cost Price of Sold Articles} = 60\% \text{ of } 123684 = 0.6 \times 123684 = 74210.4 \]

### Step 3: Calculate the selling price of the sold articles
The profit percentage on the sold articles is 16.66%. To find the selling price (SP) of these articles, we can use the formula:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
Where:
\[ \text{Profit} = \text{Cost Price} \times \frac{\text{Profit Percentage}}{100} = 74210.4 \times \frac{16.66}{100} = 12384.73 \]
Thus, the selling price of the sold articles is:
\[ \text{Selling Price} = 74210.4 + 12384.73 = 86595.13 \]

### Step 4: Calculate the total cost price of the remaining articles
The remaining articles constitute 40% of the total articles. Therefore, the cost price of the remaining articles is:
\[ \text{Cost Price of Remaining Articles} = 40\% \text{ of } 123684 = 0.4 \times 123684 = 49473.6 \]

### Step 5: Calculate the overall loss
The overall loss is given as 14%. Therefore, the total selling price (SP) for all articles can be calculated as follows:
\[ \text{Total Selling Price} = \text{Total Cost Price} - \text{Loss} \]
Where:
\[ \text{Loss} = \text{Total Cost Price} \times \frac{\text{Loss Percentage}}{100} = 123684 \times \frac{14}{100} = 17315.76 \]
Thus, the total selling price is:
\[ \text{Total Selling Price} = 123684 - 17315.76 = 106368.24 \]

### Step 6: Calculate the selling price of the remaining articles
The selling price of the remaining articles can be calculated as:
\[ \text{Selling Price of Remaining Articles} = \text{Total Selling Price} - \text{Selling Price of Sold Articles} \]
\[ \text{Selling Price of Remaining Articles} = 106368.24 - 86595.13 = 19773.11 \]

### Step 7: Calculate the loss on the remaining articles
The loss on the remaining articles can be calculated as:
\[ \text{Loss} = \text{Cost Price of Remaining Articles} - \text{Selling Price of Remaining Articles} \]
\[ \text{Loss} = 49473.6 - 19773.11 = 29600.49 \]

### Step 8: Calculate the loss percentage on the remaining articles
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price of Remaining Articles}} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{29600.49}{49473.6} \right) \times 100 \approx 59.84\% \]

### Final Answer
The loss percentage on the remaining articles is approximately **59.84%**.

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