An article passing through two hands is sold at a profit of 40% at the original cost price.If the 1st dealer makes a profit of 20%, then the profit per cent made by the second is

Options

A. `15(2)/(3)%`
B. `16(2)/(3)%`
C. `13(2)/(3)%`
D. `11(2)/(3)%`

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the problem
We have an article that is sold at a profit of 40% over its original cost price. The first dealer sells it at a profit of 20%. We need to find out the profit percentage made by the second dealer.

### Step 2: Define the original cost price
Let the original cost price (CP) of the article be 100 units.

### Step 3: Calculate the final selling price after the overall profit
The overall profit is 40% of the original cost price.
- Profit = 40% of 100 = 40 units
- Therefore, the final selling price (SP) = Original CP + Profit = 100 + 40 = 140 units.

### Step 4: Calculate the selling price of the first dealer
The first dealer makes a profit of 20% on the original cost price.
- Profit for the first dealer = 20% of 100 = 20 units
- Selling price for the first dealer = Original CP + Profit = 100 + 20 = 120 units.

### Step 5: Determine the cost price for the second dealer
The selling price of the first dealer (120 units) becomes the cost price for the second dealer.
- Cost Price for the second dealer = 120 units.

### Step 6: Calculate the profit made by the second dealer
The second dealer sells the article for 140 units (the overall selling price).
- Profit for the second dealer = Selling Price - Cost Price = 140 - 120 = 20 units.

### Step 7: Calculate the profit percentage for the second dealer
To find the profit percentage for the second dealer:
- Profit Percentage = (Profit / Cost Price) × 100
- Profit Percentage = (20 / 120) × 100 = (1/6) × 100 = 16.67%.

### Step 8: Finalize the answer
The profit percentage made by the second dealer is 16.67%, which can also be expressed as \(16 \frac{2}{3}\%\).

### Summary of the solution:
The profit percentage made by the second dealer is \(16 \frac{2}{3}\%\).

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