A shopkeeper marks his goods 20% above the CP and gives 10% discount to the customers. At the time of selling the goods he uses 900 gm weight instead of 1 kg and at the time of bying he uses 1100 gm instead of 1 kg. Find his profit.

Options

A. 0.32
B. 0.31
C. 0.33
D. 0.35

Answer

To find the profit made by the shopkeeper, we will go through the problem step by step.

### Step 1: Determine the Cost Price (CP)
Let’s assume the Cost Price (CP) of 1 kg of goods is \( CP \).

### Step 2: Calculate the Marked Price (MP)
The shopkeeper marks his goods 20% above the CP. Therefore, the Marked Price (MP) can be calculated as:
\[ MP = CP + 0.20 \times CP = 1.20 \times CP \]

### Step 3: Calculate the Selling Price (SP)
The shopkeeper gives a 10% discount on the Marked Price. Thus, the Selling Price (SP) is:
\[ SP = MP - 0.10 \times MP = 0.90 \times MP = 0.90 \times (1.20 \times CP) = 1.08 \times CP \]

### Step 4: Determine the effective weight sold
The shopkeeper sells 900 grams instead of 1 kg (1000 grams). Therefore, the Selling Price for 900 grams is:
\[ SP_{900g} = 1.08 \times CP \]

### Step 5: Determine the effective weight bought
The shopkeeper buys 1100 grams instead of 1 kg (1000 grams). Therefore, the Cost Price for 1100 grams is:
\[ CP_{1100g} = CP \times \frac{1100}{1000} = 1.1 \times CP \]

### Step 6: Calculate the total cost for 900 grams
To find the cost price for 900 grams, we can calculate it as follows:
\[ CP_{900g} = CP \times \frac{900}{1000} = 0.9 \times CP \]

### Step 7: Calculate the Profit
Now we can calculate the profit made by the shopkeeper:
\[ \text{Profit} = SP_{900g} - CP_{900g} \]
Substituting the values we have:
\[ \text{Profit} = (1.08 \times CP) - (0.9 \times CP) = 0.18 \times CP \]

### Step 8: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the profit we calculated:
\[ \text{Profit Percentage} = \left( \frac{0.18 \times CP}{0.9 \times CP} \right) \times 100 = \left( \frac{0.18}{0.9} \right) \times 100 = 20\% \]

### Final Answer
The profit percentage of the shopkeeper is **20%**.