The profit percentage of A and B is same on selling the articles at ₹ 1800 each but A calculates his profit on the selling price while B calculates it correctly on the cost price which is equal to`20%`. What is the difference in their profits?

Options

A. ₹ 360
B. ₹ 60
C. ₹ 540
D. ₹ 450

Answer

To solve the problem, we need to find the difference in profits between A and B when both sell articles at ₹1800 each, but they calculate their profits differently.

### Step-by-Step Solution:

1. **Understanding the Profit Calculation**:
- A calculates his profit based on the selling price (SP).
- B calculates his profit based on the cost price (CP) and his profit percentage is 20%.

2. **Calculating B's Cost Price**:
- Since B's profit percentage is 20%, we can express this as:
\[ \text{Profit} = \text{CP} \times \frac{20}{100} = 0.2 \times \text{CP} \]
- The selling price for B is given as ₹1800. Therefore, we can write:
\[ \text{SP} = \text{CP} + \text{Profit} \]
\[ 1800 = \text{CP} + 0.2 \times \text{CP} \]
- This simplifies to:
\[ 1800 = 1.2 \times \text{CP} \]
- Solving for CP:
\[ \text{CP} = \frac{1800}{1.2} = 1500 \]

3. **Calculating B's Profit**:
- Now that we have B's CP, we can calculate his profit:
\[ \text{Profit}_B = \text{SP} - \text{CP} = 1800 - 1500 = 300 \]

4. **Calculating A's Profit**:
- A calculates his profit based on the selling price. Since he has the same profit percentage as B (20%), we can express A's profit as:
\[ \text{Profit}_A = \text{SP} \times \frac{20}{100} = 1800 \times 0.2 = 360 \]

5. **Finding the Difference in Profits**:
- Now we can find the difference between A's and B's profits:
\[ \text{Difference} = \text{Profit}_A - \text{Profit}_B = 360 - 300 = 60 \]

### Final Answer:
The difference in their profits is ₹60.

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