A tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percent altogether.

Options

A. `14.875%`
B. `15.375%`
C. `15.575%`
D. `16.375%`

Answer

To solve the problem step by step, we will break down the information provided and calculate the gain percent altogether.

### Step 1: Define the Cost Price
Let the cost price (CP) of the goods be \(100\) rupees.

**Hint:** Start with a simple value for CP to make calculations easier.

### Step 2: Calculate the Selling Price
The selling price (SP) is fixed at 30% above the cost price. Therefore, the marked price (MP) is calculated as follows:

\[ MP = CP + 30\% \text{ of } CP = 100 + 30\% \text{ of } 100 = 100 + 30 = 130 \text{ rupees} \]

**Hint:** Remember that the selling price is based on a percentage increase from the cost price.

### Step 3: Determine the Stock Distribution
Assume the total stock is \(x\). The tradesman sells:
- Half of the stock at the marked price: \(\frac{x}{2}\)
- One quarter of the stock at a 15% discount: \(\frac{x}{4}\)
- The remaining stock at a 30% discount: \(\frac{x}{4}\)

**Hint:** Visualize the stock distribution as fractions of the total stock.

### Step 4: Calculate Selling Price for Each Portion of Stock
1. **Selling Half the Stock at MP:**
\[ SP_1 = \frac{x}{2} \times 130 = 65x \]

2. **Selling One Quarter of the Stock at 15% Discount:**
The selling price after a 15% discount on the marked price is:
\[ SP_2 = \frac{x}{4} \times (130 - 15\% \text{ of } 130) = \frac{x}{4} \times (130 - 19.5) = \frac{x}{4} \times 110.5 = 27.625x \]

3. **Selling the Remaining One Quarter at 30% Discount:**
The selling price after a 30% discount on the marked price is:
\[ SP_3 = \frac{x}{4} \times (130 - 30\% \text{ of } 130) = \frac{x}{4} \times (130 - 39) = \frac{x}{4} \times 91 = 22.75x \]

**Hint:** Discounts reduce the selling price, so calculate the new price after applying the discount.

### Step 5: Calculate Total Selling Price
Now, we can find the total selling price (SP) by adding the selling prices from all portions:

\[ SP = SP_1 + SP_2 + SP_3 = 65x + 27.625x + 22.75x = 115.375x \]

**Hint:** Combine all parts to find the total selling price.

### Step 6: Calculate Total Cost Price
The total cost price (CP) of the stock is:
\[ CP = 100x \]

**Hint:** The total cost price is simply the cost price per unit multiplied by the total number of units.

### Step 7: Calculate Profit
The profit can be calculated as:
\[ \text{Profit} = SP - CP = 115.375x - 100x = 15.375x \]

**Hint:** Profit is the difference between total selling price and total cost price.

### Step 8: Calculate Gain Percent
The gain percent is calculated using the formula:
\[ \text{Gain Percent} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{15.375x}{100x}\right) \times 100 = 15.375\% \]

**Hint:** Gain percent is a measure of profit relative to the cost price.

### Final Answer
The gain percent altogether is **15.375%**.