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 B/W 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 can use the concept of alligation, which helps us find the ratio of two quantities based on their respective gains or losses.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Total TV sets sold = 315
- Loss on black and white (B/W) TV sets = 6%
- Profit on color TV sets = 15%
- Overall gain = 9%

2. **Setting Up the Alligation**:
- We can represent the situation using the alligation formula. The loss and profit percentages can be arranged as follows:
- Loss on B/W TVs = -6%
- Gain on Color TVs = +15%
- Overall Gain = +9%

3. **Calculating the Differences**:
- Difference between the gain on color TVs and overall gain:
\[ 15\% - 9\% = 6\% \]
- Difference between overall gain and loss on B/W TVs:
\[ 9\% - (-6\%) = 9\% + 6\% = 15\% \]

4. **Setting Up the Ratio**:
- The ratio of the number of B/W TVs to the number of color TVs can be expressed as:
\[ \text{Ratio} = \frac{6}{15} = \frac{2}{5} \]

5. **Calculating the Parts**:
- Let the number of B/W TVs be \(2x\) and the number of color TVs be \(5x\).
- Total TVs sold:
\[ 2x + 5x = 315 \]
\[ 7x = 315 \]
\[ x = \frac{315}{7} = 45 \]

6. **Finding the Number of B/W TVs**:
- Now, substituting \(x\) back to find the number of B/W TVs:
\[ \text{Number of B/W TVs} = 2x = 2 \times 45 = 90 \]

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

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