A trader marks up the goods by `40%` and allows a discount of `26.67%` on the marked price. If he objects a decent `120%` profit on the goods sold, how much- per-cent more does his balance display the weight than what it displays when it is not faulty?

Options

A. 14.28
B. 53.33
C. 114.28
D. 46.67

Answer

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

### Step 1: Understand the Cost Price and Marked Price
Assume the cost price (CP) of the goods is `100` (for simplicity).

### Step 2: Calculate the Marked Price (MP)
The trader marks up the goods by `40%`. Therefore, the marked price can be calculated as:
\[ \text{Marked Price (MP)} = \text{Cost Price (CP)} + 40\% \text{ of CP} = 100 + 0.40 \times 100 = 100 + 40 = 140 \]

### Step 3: Calculate the Selling Price (SP) after Discount
The trader allows a discount of `26.67%` on the marked price. The discount amount can be calculated as:
\[ \text{Discount} = 26.67\% \text{ of MP} = 0.2667 \times 140 = 37.338 \]
Now, we can find the selling price:
\[ \text{Selling Price (SP)} = \text{MP} - \text{Discount} = 140 - 37.338 = 102.662 \]

### Step 4: Calculate the Profit
The trader claims to achieve a profit of `120%` on the cost price. The profit amount can be calculated as:
\[ \text{Profit} = 120\% \text{ of CP} = 1.20 \times 100 = 120 \]
Thus, the selling price based on the claimed profit should be:
\[ \text{Selling Price (SP)} = \text{CP} + \text{Profit} = 100 + 120 = 220 \]

### Step 5: Determine the Actual Weight Sold
From the calculations, we see that the trader is selling the goods for `220` but is actually selling them for `102.662`. This discrepancy indicates that the trader is manipulating the weight.

### Step 6: Calculate the Actual Weight
Let’s denote the actual weight sold as `x` grams. The cost price for `x` grams at `1` rupee per gram is `x`. Thus:
\[ \text{Selling Price} = \text{Cost Price for x grams} + \text{Profit} \Rightarrow 220 = x + 120 \]
Solving for `x`:
\[ x = 220 - 120 = 100 \]

### Step 7: Calculate the Faulty Weight
The trader is supposed to sell `75` grams (as per the original cost price of `75` rupees). However, he is actually selling `100` grams.

### Step 8: Calculate the Percentage Increase in Weight
The percentage increase in weight can be calculated as:
\[ \text{Percentage Increase} = \left(\frac{\text{Actual Weight} - \text{Expected Weight}}{\text{Expected Weight}}\right) \times 100 = \left(\frac{100 - 75}{75}\right) \times 100 = \left(\frac{25}{75}\right) \times 100 = \frac{1}{3} \times 100 \approx 33.33\% \]

### Final Answer
The trader's balance displays approximately `33.33%` more weight than what it should display when it is not faulty.

---