A shopkeeper sells a transistors at 15% above its cost price. If he had bought it at 5% more than what he paid for it and sold it for 6 Rs. more, he would have gained 10%. The cost price of the transistor is

Options

A. 800
B. 1000
C. 1200
D. 1400

Answer

To solve the problem step by step, let's denote the cost price of the transistor as \( CP \).

1. **Selling Price Calculation**:
The shopkeeper sells the transistor at 15% above its cost price.
\[ SP = CP + 0.15 \times CP = 1.15 \times CP \]

2. **New Cost Price Calculation**:
If the shopkeeper had bought it at 5% more than the original cost price, the new cost price would be:
\[ New \, CP = CP + 0.05 \times CP = 1.05 \times CP \]

3. **New Selling Price Calculation**:
If he sells it for Rs. 6 more than the original selling price, the new selling price would be:
\[ New \, SP = SP + 6 = 1.15 \times CP + 6 \]

4. **Profit Calculation**:
According to the problem, if he sold it at this new selling price, he would gain 10%. Therefore, the new selling price can also be expressed as:
\[ New \, SP = New \, CP + 0.10 \times New \, CP = 1.10 \times New \, CP \]

5. **Setting Up the Equation**:
We can set the two expressions for the new selling price equal to each other:
\[ 1.15 \times CP + 6 = 1.10 \times (1.05 \times CP) \]

6. **Expanding and Simplifying**:
Expanding the right side:
\[ 1.15 \times CP + 6 = 1.155 \times CP \]
Now, rearranging the equation:
\[ 6 = 1.155 \times CP - 1.15 \times CP \]
\[ 6 = 0.005 \times CP \]

7. **Solving for CP**:
Now, we can solve for \( CP \):
\[ CP = \frac{6}{0.005} = 1200 \]

Thus, the cost price of the transistor is \( \text{Rs. } 1200 \).