A shopkeeper promise to sell his goods at x% loss but he uses 20% less weight than gain 20%. Find x.

Options

A. 0.08
B. 0.12
C. 0.11
D. 0.04

Answer

To solve the problem step by step, we will analyze the situation described in the question.

### Step 1: Understand the Problem
The shopkeeper claims to sell his goods at a loss of x%, but he uses 20% less weight, which allows him to gain a profit of 20%. We need to find the value of x.

### Step 2: Assume Values
Let's assume the cost price (CP) of 100 grams of goods is 100 rupees. This makes calculations easier.

### Step 3: Calculate Selling Price (SP) at x% Loss
If the shopkeeper sells at x% loss, the selling price (SP) can be calculated as:
\[ SP = CP - (x\% \text{ of } CP) \]
\[ SP = 100 - \frac{x}{100} \times 100 \]
\[ SP = 100 - x \]

### Step 4: Determine Actual Weight Sold
Since the shopkeeper uses 20% less weight, the actual weight sold is:
\[ \text{Actual Weight} = 100 - 20\% \text{ of } 100 = 100 - 20 = 80 \text{ grams} \]

### Step 5: Calculate the Cost Price for Actual Weight
The cost price for 80 grams (which is the actual weight sold) is:
\[ \text{CP for 80 grams} = 80 \text{ grams cost } = \frac{80}{100} \times 100 = 80 \text{ rupees} \]

### Step 6: Calculate Selling Price with 20% Gain
The shopkeeper gains 20% on the cost price of 80 rupees. Therefore, the selling price (SP) for 80 grams is:
\[ SP = CP + (20\% \text{ of } CP) \]
\[ SP = 80 + \frac{20}{100} \times 80 \]
\[ SP = 80 + 16 = 96 \text{ rupees} \]

### Step 7: Set the Selling Prices Equal
Now, we have two expressions for selling price:
1. From the x% loss: \( SP = 100 - x \)
2. From the 20% gain: \( SP = 96 \)

Setting them equal gives:
\[ 100 - x = 96 \]

### Step 8: Solve for x
To find x, rearrange the equation:
\[ x = 100 - 96 \]
\[ x = 4 \]

### Conclusion
The value of x is 4%.