A trader sells total 315 TV sets. He sells black and white TV sets at a loss of 6% and colour TV sets at a profit of 15%. Thus he gains 9% on the whole. The no. of Black and white TV sets, which he has sold, is :

Options

A. 126
B. 216
C. 135
D. 90

Answer

To solve the problem step by step, we will use the concept of alligation to find the number of black and white TV sets sold by the trader.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Total TV sets sold = 315
- Loss on black and white TV sets = 6%
- Profit on color TV sets = 15%
- Overall profit = 9%

2. **Set Up the Alligation:**
- We will use the alligation method to find the ratio of the quantities of black and white TV sets and color TV sets.
- The profit/loss percentages can be arranged as follows:
- Loss on black and white TVs = -6%
- Overall profit = 9%
- Profit on color TVs = 15%

3. **Calculate the Differences:**
- Difference between profit on color TVs and overall profit:
\[ 15\% - 9\% = 6\% \]
- Difference between overall profit and loss on black and white TVs:
\[ 9\% - (-6\%) = 9\% + 6\% = 15\% \]

4. **Set Up the Ratio:**
- The ratio of the quantities of black and white TV sets to color TV sets is given by the differences calculated:
\[ \text{Ratio} = \frac{6}{15} = \frac{2}{5} \]
- This means for every 2 black and white TV sets, there are 5 color TV sets.

5. **Calculate Total Parts:**
- Total parts = 2 (black and white) + 5 (color) = 7 parts.

6. **Find the Value of One Part:**
- Since the total number of TV sets sold is 315, we can find the value of one part:
\[ \text{Value of one part} = \frac{315}{7} = 45 \]

7. **Calculate the Number of Black and White TV Sets:**
- The number of black and white TV sets sold (which corresponds to 2 parts) is:
\[ \text{Number of black and white TV sets} = 2 \times 45 = 90 \]

### Final Answer:
The number of black and white TV sets sold by the trader is **90**.

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