A bought a tape recorder for Rs 8,000 and sold it to B. B in turn sold it to C, each earning a profit of 20%. Which of the following is true:

Options

A. A and B earn the same profit.
B. A earns more profit than B.
C. A earns less profit than B.
D. Cannot be decided.

Answer

To solve the problem step by step, we will calculate the selling prices for both A and B after they earn a profit of 20% on their respective cost prices.

### Step 1: Calculate the Selling Price of A
A bought the tape recorder for Rs. 8,000. A sells it to B at a profit of 20%.

1. **Cost Price of A (CP_A)** = Rs. 8,000
2. **Profit Percentage** = 20%

To find the Selling Price (SP_A) for A:
\[ \text{Profit} = \text{CP_A} \times \frac{\text{Profit Percentage}}{100} = 8000 \times \frac{20}{100} = 8000 \times 0.2 = Rs. 1,600 \]
\[ \text{SP_A} = \text{CP_A} + \text{Profit} = 8000 + 1600 = Rs. 9,600 \]

### Step 2: Calculate the Selling Price of B
B bought the tape recorder from A for Rs. 9,600 and sells it to C at a profit of 20%.

1. **Cost Price of B (CP_B)** = Rs. 9,600
2. **Profit Percentage** = 20%

To find the Selling Price (SP_B) for B:
\[ \text{Profit} = \text{CP_B} \times \frac{\text{Profit Percentage}}{100} = 9600 \times \frac{20}{100} = 9600 \times 0.2 = Rs. 1,920 \]
\[ \text{SP_B} = \text{CP_B} + \text{Profit} = 9600 + 1920 = Rs. 11,520 \]

### Step 3: Calculate the Profits for A and B
Now we can calculate the profits for both A and B.

1. **Profit for A**:
\[ \text{Profit_A} = \text{SP_A} - \text{CP_A} = 9600 - 8000 = Rs. 1,600 \]

2. **Profit for B**:
\[ \text{Profit_B} = \text{SP_B} - \text{CP_B} = 11520 - 9600 = Rs. 1,920 \]

### Conclusion
- Profit for A = Rs. 1,600
- Profit for B = Rs. 1,920

Since Rs. 1,600 (profit for A) is less than Rs. 1,920 (profit for B), we conclude that:
**A had less profit than B.**

### Final Answer
The correct statement is: A had less profit than B.

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