The cost price of an article ‘A’ is ₹ 160 and selling price of another article B is ₹ 240. If the selling price of A will be equal to the cost price of B, then, the profit after selling A is `20%` What is the profit on ‘B ’?

Options

A. `16.66%`
B. `50%`
C. `25%`
D. none of these

Answer

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

### Step 1: Identify the Cost Price of Article A
The cost price (CP) of article A is given as ₹160.

### Step 2: Calculate the Selling Price of Article A
Since the profit after selling article A is 20%, we can calculate the selling price (SP) of article A using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where:
\[ \text{Profit} = \frac{20}{100} \times \text{CP} \]
Calculating the profit:
\[ \text{Profit} = \frac{20}{100} \times 160 = 32 \]
Now, calculate the selling price:
\[ \text{SP of A} = 160 + 32 = 192 \]

### Step 3: Determine the Selling Price of Article A Equals Cost Price of Article B
According to the problem, the selling price of article A is equal to the cost price of article B. Therefore:
\[ \text{CP of B} = \text{SP of A} = 192 \]

### Step 4: Identify the Selling Price of Article B
The selling price of article B is given as ₹240.

### Step 5: Calculate the Profit on Article B
Now we can calculate the profit on article B using the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values:
\[ \text{Profit on B} = 240 - 192 = 48 \]

### Step 6: Calculate the Profit Percentage on Article B
To find the profit percentage on article B, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage on B} = \left( \frac{48}{192} \right) \times 100 = 25\% \]

### Final Answer
The profit on article B is ₹48, and the profit percentage is 25%.

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