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.

If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?

The correct option is 5.

Let's analyze the given data and set up a systematic table to solve the problem step-by-step.

The company sells two variants of ACs: Window and Split.
Each variant can be either Inverter or Non-inverter.
Let:
- $W_I$ = Window Inverter ACs
- $W_N$ = Window Non-inverter ACs
- $S_I$ = Split Inverter ACs
- $S_N$ = Split Non-inverter ACs

Step 1: Determine total counts from the percentages and given totals
From Info 3:
Total Window Non-inverter ACs sold ($W_N$) = 6
Total Split Inverter ACs sold ($S_I$) = 36

Let the total number of ACs sold in the city be $T$.
- Window ACs ($W$) = 25% of $T$ = $0.25T$
- Split ACs ($S$) = 75% of $T$ = $0.75T$

Among the Inverter ACs sold, 20% were Window.
Let $I$ be the total number of Inverter ACs sold.
- Window Inverter ($W_I$) = $0.20I$
- Split Inverter ($S_I$) = $0.80I$

Since we are given that the total Split Inverter ACs sold is 36 ($S_I=36$):
$0.80I=36\Rightarrow I=\frac{36}{0.80}=45$
So, the total Window Inverter ACs sold is:
$W_I=0.20\times 45=9$

Now we have:
- Total Window ACs sold ($W$) = $W_I+W_N=9+6=15$

Since Window ACs are 25% of the total ACs ($T$):
$0.25T=15\Rightarrow T=60$
- Total Split ACs sold ($S$) = $60-15=45$
- Total Split Non-inverter ACs sold ($S_N$) = $S-S_I=45-36=9$
- Total Non-inverter ACs sold ($N$) = $T-I=60-45=15$

Step 2: Distribute AC sales among the dealers
Let us analyze the clues for Window ACs first:
- From Info 4 (second version in the numbered list): "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."
Since the total Window Non-inverter ACs ($W_N$) is 6, we have:
$W_N\left(\text{D2}\right)+W_N\left(\text{D3}\right)=6$
With $W_N\left(\text{D2}\right)=2\times W_N\left(\text{D3}\right)$, this gives:
$W_N\left(\text{D2}\right)=4$
$W_N\left(\text{D3}\right)=2$
$W_N\left(\text{D1}\right)=W_N\left(\text{D4}\right)=0$

- From Info 5 (first version): "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."
Let $W\left(\text{D3}\right)=W\left(\text{D4}\right)=k$ and $W\left(\text{D2}\right)=3k$.
Since the total number of Window ACs sold is 15:
$W\left(\text{D1}\right)+W\left(\text{D2}\right)+W\left(\text{D3}\right)+W\left(\text{D4}\right)=15$
$W\left(\text{D1}\right)+3k+k+k=15\Rightarrow W\left(\text{D1}\right)+5k=15$
Since every dealer sold at least two window ACs (Info 1), we have $W\left(\text{D1}\right)\ge 2$ and $k\ge 2$.
If $k=2$:
$W\left(\text{D1}\right)=15-10=5$ (which is valid).
If $k\ge 3$, then $5k\ge 15$, which would mean $W\left(\text{D1}\right)\le 0$ (violating the minimum limit of 2).
Thus, we must have $k=2$. Therefore:
- $W\left(\text{D1}\right)=5$
- $W\left(\text{D2}\right)=6$
- $W\left(\text{D3}\right)=2$
- $W\left(\text{D4}\right)=2$

Since we already know the Window Non-inverter ($W_N$) counts for each dealer, we can find their Window Inverter ($W_I$) counts using $W_I=W-W_N$:
- $W_I\left(\text{D1}\right)=5-0=5$
- $W_I\left(\text{D2}\right)=6-4=2$
- $W_I\left(\text{D3}\right)=2-2=0$
- $W_I\left(\text{D4}\right)=2-0=2$

Step 3: Analyze Split Inverter ACs ($S_I$)
From Info 5 (second version): "D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2."
Let $S_I\left(\text{D3}\right)=S_I\left(\text{D4}\right)=y$ and $S_I\left(\text{D2}\right)=2y$.
The total Split Inverter ACs sold is 36:
$S_I\left(\text{D1}\right)+S_I\left(\text{D2}\right)+S_I\left(\text{D3}\right)+S_I\left(\text{D4}\right)=36$
$S_I\left(\text{D1}\right)+2y+y+y=36\Rightarrow S_I\left(\text{D1}\right)+4y=36$

From Info 2: "D1 sold 13 inverter ACs."
The total inverter ACs sold by D1 is $W_I\left(\text{D1}\right)+S_I\left(\text{D1}\right)=13$.
Since $W_I\left(\text{D1}\right)=5$, we have:
$S_I\left(\text{D1}\right)=13-5=8$

Substitute $S_I\left(\text{D1}\right)=8$ into the equation:
$8+4y=36\Rightarrow 4y=28\Rightarrow y=7$

So, the Split Inverter counts are:
- $S_I\left(\text{D1}\right)=8$
- $S_I\left(\text{D2}\right)=14$
- $S_I\left(\text{D3}\right)=7$
- $S_I\left(\text{D4}\right)=7$

Step 4: Analyze Split ACs and Non-inverter ACs
From Info 4 (first version): "The number of Split ACs sold by D1 was twice the number of Window ACs sold by it."
- $W\left(\text{D1}\right)=5\Rightarrow S\left(\text{D1}\right)=2\times 5=10$
Since $S\left(\text{D1}\right)=S_I\left(\text{D1}\right)+S_N\left(\text{D1}\right)$, and we know $S_I\left(\text{D1}\right)=8$:
- $S_N\left(\text{D1}\right)=10-8=2$

From Info 2: "D3 sold 5 Non-inverter ACs."
Total Non-inverter ACs sold by D3 is $W_N\left(\text{D3}\right)+S_N\left(\text{D3}\right)=5$.
Since $W_N\left(\text{D3}\right)=2$, we have:
- $S_N\left(\text{D3}\right)=5-2=3$

Step 5: Calculate total ACs for D3 and D4 to find the remaining values
Let's find the total ACs sold by D3:
$\text{Total ACs (D3)}=W\left(\text{D3}\right)+S\left(\text{D3}\right)=2+\left(S_I\right(\text{D3})+S_N(\text{D3}\left)\right)=2+(7+3)=12$

The problem states: "If D3 and D4 sold an equal number of ACs..."
Therefore, $\text{Total ACs (D4)}=\text{Total ACs (D3)}=12$.
For D4, we know:
- $W\left(\text{D4}\right)=2$
- $S_I\left(\text{D4}\right)=7$
- $S_N\left(\text{D4}\right)=12-W\left(\text{D4}\right)-S_I\left(\text{D4}\right)=12-2-7=3$

Now we can determine the Split Non-inverter ACs sold by D2 ($S_N\left(\text{D2}\right)$).
Since the total Split Non-inverter ACs sold in the city is 9:
$S_N\left(\text{D1}\right)+S_N\left(\text{D2}\right)+S_N\left(\text{D3}\right)+S_N\left(\text{D4}\right)=9$
$2+S_N\left(\text{D2}\right)+3+3=9\Rightarrow 8+S_N\left(\text{D2}\right)=9\Rightarrow S_N\left(\text{D2}\right)=1$

Finally, we calculate the number of Non-inverter ACs sold by D2:
$\text{Non-inverter ACs (D2)}=W_N\left(\text{D2}\right)+S_N\left(\text{D2}\right)=4+1=5$

Thus, the number of Non-inverter ACs sold by D2 is 5.