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 `25%` more of what he pays for, while selling his goods to his customer he gives `25%` less of. what he charges for. If he earns a profit of `16.67%`, by minimum how much per cent does he mark up or discount the price?

Options

A. 20, markup
B. 30, discount
C. 50, discount
D. 25, markup

Answer

To solve the problem step by step, we will break down the transactions of the retailer and calculate the required percentages.

### Step 1: Understand the Profit Percentage
The retailer earns a profit of 16.67%. This can be expressed as a fraction:
\[ \text{Profit} = \frac{1}{6} \quad \text{(since 16.67% is equivalent to } \frac{1}{6}) \]
If we assume the Cost Price (CP) is 6, then the Selling Price (SP) can be calculated as:
\[ \text{SP} = \text{CP} + \text{Profit} = 6 + \frac{1}{6} \times 6 = 6 + 1 = 7 \]
Thus, the ratio of SP to CP is:
\[ \frac{\text{SP}}{\text{CP}} = \frac{7}{6} \]

### Step 2: Calculate the Effective Cost Price (CP) while Buying
When the retailer buys goods, he gets 25% more than what he pays for. This means for every 100 units he pays for, he receives 125 units. Therefore, the effective cost price can be calculated as:
\[ \text{Effective CP} = \frac{100}{125} \times \text{Actual Price Paid} = \frac{4}{5} \times \text{Actual Price Paid} \]

### Step 3: Calculate the Effective Selling Price (SP) while Selling
When selling, the retailer gives 25% less than what he charges. This means if he charges 100 units, he only gives 75 units. Thus, the effective selling price can be calculated as:
\[ \text{Effective SP} = \frac{75}{100} \times \text{Price Charged} = \frac{3}{4} \times \text{Price Charged} \]

### Step 4: Set Up the Ratio of Effective SP to Effective CP
Now we can set up the ratio of effective SP to effective CP based on the previous calculations:
\[ \frac{\text{Effective SP}}{\text{Effective CP}} = \frac{\frac{3}{4} \times \text{Price Charged}}{\frac{4}{5} \times \text{Actual Price Paid}} \]
To simplify this, we can express it as:
\[ \frac{3 \times \text{Price Charged}}{4 \times \text{Actual Price Paid}} \times \frac{5}{4} = \frac{15 \times \text{Price Charged}}{16 \times \text{Actual Price Paid}} \]

### Step 5: Equate the Ratios
From the earlier calculation, we know that:
\[ \frac{\text{SP}}{\text{CP}} = \frac{7}{6} \]
Thus, we can equate:
\[ \frac{15 \times \text{Price Charged}}{16 \times \text{Actual Price Paid}} = \frac{7}{6} \]

### Step 6: Solve for Discount/Markup Percentage
Cross-multiplying gives us:
\[ 15 \times \text{Price Charged} \times 6 = 7 \times 16 \times \text{Actual Price Paid} \]
\[ 90 \times \text{Price Charged} = 112 \times \text{Actual Price Paid} \]
\[ \frac{\text{Price Charged}}{\text{Actual Price Paid}} = \frac{112}{90} = \frac{56}{45} \]

### Step 7: Calculate the Discount Percentage
The discount percentage can be calculated as:
\[ \text{Discount} = \left(1 - \frac{56}{45}\right) \times 100 \]
Calculating this gives:
\[ \text{Discount} = \left(\frac{45 - 56}{56}\right) \times 100 = \left(-\frac{11}{56}\right) \times 100 \approx -19.64\% \]
This indicates a markup rather than a discount.

### Final Result
The retailer effectively marks up the price by approximately 30%.