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

The correct Option is(D): 14 AC's.
Here's a simplified explanation of the solution:
Total ACs Sold (A):
Window ACs: 25% of A → \(\frac{A}{4}\)​
Split ACs: 75% of A → \(\frac{3A}{4}\)​
Total Inverter ACs (B):
Window Inverter ACs: 20% of B → \(\frac{B}{5}\)​
Split Inverter ACs: 80% of B → \(\frac{4B}{5}\)​
Conditions Given:
Total Window Non-Inverter ACs = 6
Total Split Inverter ACs = 36
Equations from Conditions:
\(\frac{A}{4}-\frac{B}{5}\)​=6
\(\frac{4B}{5}\)​=36
Solving the Equations:
\(\frac{4B}{5}\)​=36 → 𝐵=45
Substitute 𝐵=45 into \(\frac{A}{4}\)−9=6:
\(\frac{A}{4}\)=15 → 𝐴=60
Distribution of ACs:
Total ACs: 60
Window ACs: 15
Split ACs: 45
Inverter ACs: 36
Non-Inverter ACs: 24
Individual Dealer Conditions:
D2 sold twice as many Window Non-Inverter ACs as D3.
D3 and D4 sold equal Window ACs, which is one-third of D2's Window ACs.
D3 and D4 sold equal Split Inverter ACs, which is half of D2's Split Inverter ACs.
Using Given Conditions to Solve:
D3's Window Non-Inverter ACs = 2
D2's Window Non-Inverter ACs = 4
Let Window ACs sold by D3 and D4 be 𝑦y:
𝐷2=3𝑦D2=3y
3𝑦+𝑦+𝑦=153y+y+y=15
5𝑦=155y=15 → 𝑦=3y=3
D3 and D4 sold 3 Window ACs each, D2 sold 9 Window ACs.
Split Inverter ACs sold by D3 and D4 = 7 each
D2 sold 2×7=142×7=14 Split Inverter ACs.
So, D2 sold 14 Split Inverter ACs.