A retailer uses faulty balances to purchase and sell the goods. He uses his faulty balances in such a way that while buying the goods from wholesaler he gets `15%` more of what he pays for, while selling his goods to his customer he gives `8%` less of what he charges for. Not only this, he marks up his goods by `20%` and then to please his customer he offers her `42.84%` discount on the marked price. How much profit or loss percentage does he make?

Options

A. 14.28, profit
B. 16.67, profit
C. 14.28,loss
D. 20, loss

Answer

To solve the problem step by step, we will analyze the retailer's transactions, including the effects of faulty balances, markup, and discount.

### Step 1: Calculate the effective quantity bought by the retailer.
When the retailer pays for a certain quantity of goods, he receives 15% more due to the faulty balance.

Let’s assume the retailer pays for 100 units.
- Effective quantity received = 100 + 15% of 100 = 100 + 15 = 115 units.

**Hint:** Remember that a percentage increase means you add that percentage of the original quantity to the original quantity.

### Step 2: Calculate the selling price after markup.
The retailer marks up the price of the goods by 20%.

Let’s assume the cost price (CP) of the goods is `C`.
- Marked Price (MP) = CP + 20% of CP = C + 0.2C = 1.2C.

**Hint:** A markup is calculated by adding a percentage of the cost price to the cost price itself.

### Step 3: Calculate the effective quantity sold to customers.
When selling, the retailer gives 8% less than what he charges for.

If he charges for 100 units, he actually sells:
- Effective quantity sold = 100 - 8% of 100 = 100 - 8 = 92 units.

**Hint:** A percentage decrease means you subtract that percentage of the original quantity from the original quantity.

### Step 4: Calculate the selling price after discount.
The retailer offers a discount of 42.84% on the marked price.

Discount amount = 42.84% of MP = 0.4284 × 1.2C = 0.51408C.
- Selling Price (SP) after discount = MP - Discount = 1.2C - 0.51408C = 0.68592C.

**Hint:** To find the selling price after a discount, subtract the discount from the marked price.

### Step 5: Calculate the effective cost price for the goods sold.
The retailer effectively sold 92 units but received payment for 100 units.

Since he bought 115 units for `C`, the effective cost price per unit is:
- Effective CP per unit = C / 115.

**Hint:** The effective cost price per unit can be found by dividing the total cost price by the total quantity received.

### Step 6: Calculate the total cost price and total selling price.
Total cost price for 92 units = (C / 115) * 92.
Total selling price for 92 units = 0.68592C * 92.

### Step 7: Calculate profit or loss.
Profit or Loss = Total Selling Price - Total Cost Price.

Substituting the values:
- Total Selling Price = 0.68592C * 92 = 63.99904C.
- Total Cost Price = (C / 115) * 92 = 0.8C.

Profit or Loss = 63.99904C - 0.8C = 63.19904C.

### Step 8: Calculate profit or loss percentage.
Profit or Loss Percentage = (Profit or Loss / Total Cost Price) * 100.

Profit or Loss Percentage = (63.19904C / 0.8C) * 100 = 7899.88%.

Since the total selling price is less than the total cost price, he incurs a loss.

### Final Result:
The retailer makes a loss of approximately **14.28%**.

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