An air conditioner (AC) company has four dealers – D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs – Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:
1. Every dealer sold at least two window ACs.
2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

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What percentage of ACs sold were of Non-inverter type?

Question

An air conditioner (AC) company has four dealers – D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs – Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:
1. Every dealer sold at least two window ACs.
2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

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What percentage of ACs sold were of Non-inverter type?

Accepted Answer

To determine the percentage of ACs sold that were Non-inverter type, we analyze the given data step by step.

### Step-by-Step Analysis:

#### Step 1: Total Sales Distribution
Let the total number of ACs sold in the city be $$ T $$. The problem states:
- **25% of total ACs sold were Window variant**, so:
  $$
  	ext{Window Sales} = 0.25T.
  $$
- **75% of total ACs sold were Split variant**, so:
  $$
  	ext{Split Sales} = 0.75T.
  $$

#### Step 2: Known Data
From the problem:
1. **6 Window Non-inverter ACs** were sold (Fact 3).
2. **36 Split Inverter ACs** were sold (Fact 3).
3. Among **Inverter ACs**, **20% were Window variant**, so:
   $$
   	ext{Window Inverter Sales} = 0.2 	imes (	ext{Total Inverter Sales}).
   $$

#### Step 3: Calculate Total Non-inverter Sales
- The total Non-inverter sales include:
   - **Window Non-inverter ACs = 6** (Fact 3),
   - **Split Non-inverter ACs = T - (	ext{Window Inverter Sales} + 	ext{Split Inverter Sales})**.

#### Step 4: Solve for Total Non-inverter Percentage
The problem specifies that **36 Split Inverter ACs** and **20% of all Inverter ACs are Window variant**, which implies:
- Total Inverter ACs = $$ 	ext{Window Inverter Sales} + 	ext{Split Inverter Sales} = (0.2 	imes T) + 36 $$.

Let $$ T = 100 $$ (assume total sales for simplicity):
- Window variant sales = $$ 25\%$$ of $$ T = 25 $$,
- Split variant sales = $$ 75\%$$ of $$ T = 75 $$.

From Fact (3):
- Window Non-inverter sales = $$6$$,
- Split Inverter sales = $$36$$,
- Remaining Split Non-inverter sales = $$75 - 36 = 39$$.

Thus, total Non-inverter sales:
$$
	ext{Non-inverter Sales} = 	ext{Window Non-inverter} + 	ext{Split Non-inverter} = 6 + 39 = 45.
$$

Percentage of Non-inverter type:
$$
\frac{	ext{Non-inverter Sales}}{	ext{Total Sales}} 	imes 100 = \frac{45}{100} 	imes 100 = 25\%.
$$

### Conclusion:
The percentage of ACs sold that were Non-inverter type is **25%**, making option **C** correct.

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