Question Details

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.

What percentage of ACs sold were of Non-inverter type?

Options

A

75%

B

20%

C

25%

D

4.33%

Show Answer

Correct Answer :

Option C

25%

Solution :

The correct answer is 25%.

Let us solve the problem step-by-step.
We are given that the company sells two variants of ACs: Window and Split.
Each variant can be either Inverter or Non-inverter.

Let the total number of ACs sold in the city be denoted by T.
From the given information:
- 25% of the total ACs sold were Window variant. Thus, Window ACs = 0.25T.
- The rest were Split variant. Thus, Split ACs = 0.75T.

Let IW and IS be the number of Inverter Window and Inverter Split ACs sold, respectively.
Let NW and NS be the number of Non-inverter Window and Non-inverter Split ACs sold, respectively.

From Point 3, we are given:
- The total number of Window Non-inverter ACs sold is NW=6.
- The total number of Split Inverter ACs sold is IS=36.

Since the total number of Window ACs is the sum of Window Inverter and Window Non-inverter ACs:
Total Window ACs=IW+NW=IW+6

We are also told that among the Inverter ACs sold, 20% were of Window variant.
The total number of Inverter ACs sold is IW+IS=IW+36.
Therefore:
IW=0.20(IW+36)
Multiplying both sides by 5:
5IW=IW+36
4IW=36
IW=9

Thus, the total number of Window ACs sold is:
Total Window ACs=IW+NW=9+6=15

Since Window ACs constitute 25% of the total ACs sold:
0.25T=15
T=60

The total number of Inverter ACs sold is:
Total Inverter ACs=IW+IS=9+36=45

Therefore, the total number of Non-inverter ACs sold is:
Total Non-inverter ACs=T-Total Inverter ACs=60-45=15

The percentage of ACs sold that were of Non-inverter type is:
1560×100%=25%

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