Comprehension:

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.

4. 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.

5. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

How many Split Inverter ACs did D2 sell?

The correct answer is 14.

Let us analyze the information given in the problem step-by-step to determine the number of Split Inverter ACs sold by D2.

Step 1: Determine the overall distribution of AC types sold in the city
Let $T$ be the total number of ACs sold in the city. From the problem statement, we have:
- Window ACs ($W$) = 25% of $T=0.25T$
- Split ACs ($S$) = 75% of $T=0.75T$
Among the Inverter ACs ($I$) sold, 20% are of Window variant. Therefore:
- Window Inverter ACs ($W_I$) = 20% of $I=0.2I$
- Split Inverter ACs ($S_I$) = 80% of $I=0.8I$

We are given that a total of 36 Split Inverter ACs were sold in the city ($S_I=36$). Using this, we can find the total number of Inverter ACs ($I$):

$0.8I=36\Rightarrow I=\frac{36}{0.8}=45$

Using this value of $I$, we find the number of Window Inverter ACs:

$W_I=0.2\times 45=9$

We are also given that a total of 6 Window Non-inverter ACs ($W_N$) were sold. Thus, the total number of Window ACs ($W$) sold is:

$W=W_I+W_N=9+6=15$

Since Window ACs make up 25% of the total ACs sold ($W=0.25T$):

$0.25T=15\Rightarrow T=60$

Step 2: Determine Window ACs sold by each dealer
Let $W\left(D\right)$ represent the number of Window ACs sold by dealer $D$.
According to condition 5, D3 and D4 sold an equal number of Window ACs, which was one-third of the number of Window ACs sold by D2:

$W\left(\mathrm{D3}\right)=W\left(\mathrm{D4}\right)=\frac{1}{3}W\left(\mathrm{D2}\right)$

The total Window ACs sold by all dealers is 15:

$W\left(\mathrm{D1}\right)+W\left(\mathrm{D2}\right)+W\left(\mathrm{D3}\right)+W\left(\mathrm{D4}\right)=15$

$W\left(\mathrm{D1}\right)+3W\left(\mathrm{D3}\right)+W\left(\mathrm{D3}\right)+W\left(\mathrm{D3}\right)=15$

$W\left(\mathrm{D1}\right)+5W\left(\mathrm{D3}\right)=15$

Condition 1 states that every dealer sold at least two Window ACs, so $W\left(\mathrm{D3}\right)\ge 2$ and $W\left(\mathrm{D1}\right)\ge 2$.
- If $W\left(\mathrm{D3}\right)=2$, then $W\left(\mathrm{D1}\right)+10=15\Rightarrow W\left(\mathrm{D1}\right)=5$. This is a valid configuration.
- If $W\left(\mathrm{D3}\right)\ge 3$, then $W\left(\mathrm{D1}\right)\le 0$, which violates the constraint.
Thus, the Window ACs sold by each dealer are:
- D1: 5 Window ACs
- D2: 6 Window ACs
- D3: 2 Window ACs
- D4: 2 Window ACs

Step 3: Analyze Window Non-inverter ACs
According to the second condition 4 (from the second set of numbered list), D2 and D3 were the only ones who sold Window Non-inverter ACs, with D2 selling twice as many as D3. Since the total is 6:
- $W_N\left(\mathrm{D2}\right)=4$
- $W_N\left(\mathrm{D3}\right)=2$
- $W_N\left(\mathrm{D1}\right)=W_N\left(\mathrm{D4}\right)=0$

This allows us to calculate the Window Inverter ACs ($W_I$) for each dealer ($W_I=W-W_N$):
- D1: $5-0=5$
- D2: $6-4=2$
- D3: $2-2=0$
- D4: $2-0=2$

Step 4: Find the Split Inverter ACs sold by D2
D1 sold 13 Inverter ACs in total. The total Inverter ACs sold by D1 is the sum of Window Inverter and Split Inverter ACs:
- $W_I\left(\mathrm{D1}\right)+S_I\left(\mathrm{D1}\right)=13$
Substituting $W_I\left(\mathrm{D1}\right)=5$:

$5+S_I\left(\mathrm{D1}\right)=13\Rightarrow S_I\left(\mathrm{D1}\right)=8$

According to the second condition 5, D3 and D4 sold an equal number of Split Inverter ACs, and this number was half the number sold by D2:
- $S_I\left(\mathrm{D3}\right)=S_I\left(\mathrm{D4}\right)=\frac{1}{2}{S}_I\left(\mathrm{D2}\right)$

The total number of Split Inverter ACs sold by all dealers is 36:

$S_I\left(\mathrm{D1}\right)+S_I\left(\mathrm{D2}\right)+S_I\left(\mathrm{D3}\right)+S_I\left(\mathrm{D4}\right)=36$

$8+S_I\left(\mathrm{D2}\right)+\frac{1}{2}{S}_I\left(\mathrm{D2}\right)+\frac{1}{2}{S}_I\left(\mathrm{D2}\right)=36$

$8+2S_I\left(\mathrm{D2}\right)=36$

$2S_I\left(\mathrm{D2}\right)=28\Rightarrow S_I\left(\mathrm{D2}\right)=14$

Thus, D2 sold 14 Split Inverter ACs.