A dealer marked up his goods 20% above its cost price and sold 75% of the goods at 25% profit and remaining at marked price, Find his overall profit percentage.

Options

A. A)`25(1)/(2)%`
B. B)`23(3)/(4)%`
C. C)`12(1)/(2)%`
D. D)`22(1)/(4)%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP) and Marked Price (MP)
- Let's assume the cost price (CP) of the goods is 100 units.
- The dealer marks up the goods by 20%. Therefore, the marked price (MP) is calculated as:
\[ MP = CP + (20\% \text{ of } CP) = 100 + (0.20 \times 100) = 100 + 20 = 120 \text{ units} \]

**Hint:** Remember that the marked price is calculated by adding the markup percentage to the cost price.

### Step 2: Calculate the Selling Price (SP) for 75% of the Goods
- The dealer sells 75% of the goods at a 25% profit. The selling price for this portion can be calculated as:
\[ SP_{75\%} = CP + (25\% \text{ of } CP) = 100 + (0.25 \times 100) = 100 + 25 = 125 \text{ units} \]

**Hint:** The selling price at a profit is calculated by adding the profit percentage to the cost price.

### Step 3: Calculate the Selling Price for the Remaining 25% of the Goods
- The remaining 25% of the goods is sold at the marked price, which is 120 units. Therefore:
\[ SP_{25\%} = MP = 120 \text{ units} \]

**Hint:** When goods are sold at marked price, the selling price equals the marked price.

### Step 4: Calculate the Total Selling Price (TSP)
- Now, we calculate the total selling price for all goods sold:
\[ TSP = (75\% \text{ of total goods} \times SP_{75\%}) + (25\% \text{ of total goods} \times SP_{25\%}) \]
Since we assumed the total goods to be 100 units:
\[ TSP = (75 \times 125) + (25 \times 120) = 9375 + 3000 = 12375 \text{ units} \]

**Hint:** To find the total selling price, multiply the quantity sold by the selling price for each portion and then sum them up.

### Step 5: Calculate the Total Cost Price (TCP)
- The total cost price for all goods is simply:
\[ TCP = 100 \text{ units} \]

**Hint:** The total cost price is the initial cost price multiplied by the total quantity of goods.

### Step 6: Calculate the Overall Profit
- The overall profit can be calculated as:
\[ \text{Profit} = TSP - TCP = 12375 - 10000 = 2375 \text{ units} \]

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

### Step 7: Calculate the Overall Profit Percentage
- The overall profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{TCP}}\right) \times 100 = \left(\frac{2375}{10000}\right) \times 100 = 23.75\% \]

**Hint:** To find the profit percentage, divide the profit by the total cost price and multiply by 100.

### Final Answer
The overall profit percentage is **23.75%** or **23 3/4%**.

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