A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price. one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is

Options

A. 2.00%
B. 4.50%
C. 13.50%
D. 15.00%

Answer

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

### Step 1: Determine the Cost Price (CP) and Marked Price (MP)
- Let's assume the cost price (CP) of each article is ₹1.
- If the trader marks his goods at 20% above the cost price, the marked price (MP) can be calculated as follows:

\[ MP = CP + (20\% \text{ of } CP) = 1 + (0.20 \times 1) = 1 + 0.20 = ₹1.20 \]

### Step 2: Calculate the Total Number of Articles
- Assume the total number of articles is 80.

### Step 3: Calculate the Total Marked Price
- The total marked price for all articles is:

\[ \text{Total MP} = \text{Number of articles} \times MP = 80 \times 1.20 = ₹96 \]

### Step 4: Calculate Sales from Different Portions of Stock
1. **Half of the stock sold at marked price:**
- Number of articles sold = \( \frac{80}{2} = 40 \)
- Selling Price (SP) for this portion:

\[ SP_1 = 40 \times 1.20 = ₹48 \]

2. **One quarter sold at a 20% discount on marked price:**
- Number of articles sold = \( \frac{80}{4} = 20 \)
- Selling Price (SP) for this portion:

\[ \text{Discount} = 20\% \text{ of } 1.20 = 0.20 \times 1.20 = ₹0.24 \]
\[ \text{Selling Price per article} = MP - \text{Discount} = 1.20 - 0.24 = ₹0.96 \]
\[ SP_2 = 20 \times 0.96 = ₹19.20 \]

3. **The rest sold at a 40% discount on marked price:**
- Number of articles sold = \( 80 - 40 - 20 = 20 \)
- Selling Price (SP) for this portion:

\[ \text{Discount} = 40\% \text{ of } 1.20 = 0.40 \times 1.20 = ₹0.48 \]
\[ \text{Selling Price per article} = MP - \text{Discount} = 1.20 - 0.48 = ₹0.72 \]
\[ SP_3 = 20 \times 0.72 = ₹14.40 \]

### Step 5: Calculate Total Selling Price (SP)
- Now, we can calculate the total selling price:

\[ \text{Total SP} = SP_1 + SP_2 + SP_3 = 48 + 19.20 + 14.40 = ₹81.60 \]

### Step 6: Calculate Total Cost Price (CP)
- The total cost price for all articles:

\[ \text{Total CP} = \text{Number of articles} \times CP = 80 \times 1 = ₹80 \]

### Step 7: Calculate Total Gain
- The total gain can be calculated as:

\[ \text{Total Gain} = \text{Total SP} - \text{Total CP} = 81.60 - 80 = ₹1.60 \]

### Step 8: Calculate Gain Percentage
- The gain percentage can be calculated as:

\[ \text{Gain Percentage} = \left( \frac{\text{Total Gain}}{\text{Total CP}} \right) \times 100 = \left( \frac{1.60}{80} \right) \times 100 = 2\% \]

### Final Answer
- The total gain is **2%**.