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. 
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
What was the total number of ACs sold by D2 and D4? (This Question was asked as TITA)

• A. 33 AC's
• B. 39 AC's
• C. 42 AC's
• D. 28 AC's

Answer 1

The Correct Option is A

To solve this problem, we break down the given conditions systematically: 

1. Let the number of Window ACs be $W$ and Split ACs be $S$.
Given: 25% of ACs are Window type, so $W = 0.25T$ and $S = 0.75T$, where $T$ is the total number of ACs sold.

2. Among Inverter ACs, 20% are Window variants. Let $I$ be the total Inverter ACs.
Then, Window Inverter ACs $= 0.2I$.

3. Dealer D1 sold 13 Inverter ACs. Also, the number of Split ACs was twice the number of Window ACs sold.
Let the number of Window ACs sold by D1 be $x$. Then Split ACs $= 2x$.
So, total ACs by D1 $= x + 2x = 3x$.

4. D3 and D4 sold an equal number of Window ACs, and each sold one-third of what D2 sold.
Let each of D3 and D4 have sold $y$ Window ACs, then D2 sold $3y$.
So total Window ACs from D2, D3, D4 $= 3y + y + y = 5y$.
Since D1 sold $x$ Window ACs and total Window ACs is $W = 7x$, we have:
$7x = 5y \Rightarrow \dfrac{x}{y} = \dfrac{5}{7}$.

5. D2 and D3 sold all the Window Non-Inverter ACs. D2 sold twice as many as D3.
Total Window Non-Inverter ACs = 6.
Let D3 sold $z$, then D2 sold $2z$. So $z + 2z = 6 \Rightarrow z = 2$, $2z = 4$.

6. Total Split Inverter ACs = 36. D3 and D4 sold equal numbers, each being half of what D2 sold.
Let D3 and D4 each sold $p$, then D2 sold $2p$.
$2p + p + p = 4p = 36 \Rightarrow p = 9$.
So D2 sold 18, D3 and D4 each sold 9 Split Inverter ACs.

Now, calculate total ACs sold by D2 and D4:

D2: Window ACs $= 3y$, Split Inverter $= 18$, Window Non-inverter $= 4$
Total for D2 $= 3y + 18 + 4 = 3y + 22$

D4: Window ACs $= y$, Split Inverter $= 9$
Total for D4 $= y + 9$

Combine both:
Total by D2 and D4 $= 3y + 22 + y + 9 = 4y + 31$

From earlier, $7x = 5y \Rightarrow x = \dfrac{5y}{7}$, so everything can be written in terms of $y$.

Thus, the total number of ACs sold by D2 and D4 is 33.