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
How many Split Inverter ACs did D2 sell?

• A. 27 AC's
• B. 22 AC's
• C. 20 AC's
• D. 14 AC's

Answer 1

The Correct Option is D

To solve this problem, we begin by analyzing the provided information and deriving equations to evaluate the sales figures.

Step-by-step Analysis: 

1. Total Window and Split ACs:
Let the total number of ACs be \( T \). Given that 25% are Window, we have:
- Window ACs: \( 0.25T \)
- Split ACs: \( 0.75T \)
Let total Inverter ACs be \( I \). Given that 20% of Inverter ACs are Window, we have:
- Window Inverter ACs: \( 0.2I \)
- Split Inverter ACs: \( 0.8I \)

2. Problem Information:
(a) There are 6 Window Non-inverter ACs.
(b) There are 36 Split Inverter ACs.

Dealer-wise Information:
(i) Dealer D1 sold 13 Inverter ACs, and Split ACs = 2 × Window ACs.
(ii) D3 sold 5 Non-inverter ACs and equal Window ACs as D4.
(iii) D2 sold twice the number of Window Non-inverter ACs as D3 ⇒ D3 = 1, D2 = 2.
(iv) Split Inverter ACs: D3 = D4 = \( \frac{1}{2} \) × D2.

3. Calculations:
(a) From (iii), total Window Non-inverter ACs = 1 (D3) + 2 (D2) = 3. But given total is 6 ⇒ the rest (3) must be with D1.
(b) Let D2 sold \( x \) Split Inverter ACs. Then D3 and D4 each sold \( \frac{x}{2} \) ACs ⇒ Total = \( x + \frac{x}{2} + \frac{x}{2} = 2x \).
Given total Split Inverter = 36 ⇒ \( 2x = 36 \Rightarrow x = 18 \). (Correction from original misstep)
But that contradicts earlier assumption. Let’s use another consistent equation.
Let D2’s Split Inverter be \( x \), then D3 + D4 = 2x.
Given D2 + D3 + D4 = 36 ⇒ \( x + 2x = 36 \Rightarrow 3x = 36 \Rightarrow x = 12 \).

4. Result:
The number of Split Inverter ACs sold by Dealer D2 is 12 ACs.