Question Details

Directions: Read the following table carefully and answer the question given below.

The table shows the total number of home appliances (Smart TVs, Refrigerators, and Air Conditioners) sold by four different retail branches and the percentage of Smart TVs sold out of the total appliances sold. The table also depicts the difference between the number of Refrigerators and Air Conditioners sold by these four branches.

Note: The number of Refrigerators sold is higher than the number of Air Conditioners sold by each branch.

Retail Branches Total number of appliances sold Percentage of Smart TVs sold Difference between Refrigerators and Air Conditioners sold

Branch P 400 25% 70

Branch Q 550 10% 85

Branch R 360 30% 52

Branch S 280 15% 102

By how much does the total number of Air Conditioners sold by Branch Q exceed or fall short of the total number of Refrigerators sold by Branch R?

Retail Branches	Total number of appliances sold	Percentage of Smart TVs sold	Difference between Refrigerators and Air Conditioners sold
Branch P	400	25%	70
Branch Q	550	10%	85
Branch R	360	30%	52
Branch S	280	15%	102

Options

Show Answer

Correct Answer :

Option A

Solution :

The correct answer is 53.

Step 1: Calculate the total number of Air Conditioners sold by Branch Q.

Total appliances sold by Branch Q = 550
Percentage of Smart TVs sold by Branch Q = 10%

Number of Smart TVs sold by Branch Q:

$10 % \times 550 = \frac{10}{100} \times 550 = 55$

Total number of Refrigerators and Air Conditioners sold together by Branch Q:

$550 - 55 = 495$

Let $R_{Q}$ be the number of Refrigerators and $A_{Q}$ be the number of Air Conditioners sold by Branch Q.
We know that the number of Refrigerators sold is higher than Air Conditioners, and the difference is 85:
$R_{Q} - A_{Q} = 85$

We also have their sum:
$R_{Q} + A_{Q} = 495$

Subtracting the difference equation from the sum equation gives:
$2 \times A_{Q} = 495 - 85 = 410$

$A_{Q} = \frac{410}{2} = 205$

Thus, the number of Air Conditioners sold by Branch Q is 205.

Step 2: Calculate the total number of Refrigerators sold by Branch R.

Total appliances sold by Branch R = 360
Percentage of Smart TVs sold by Branch R = 30%

Number of Smart TVs sold by Branch R:

$30 % \times 360 = \frac{30}{100} \times 360 = 108$

Total number of Refrigerators and Air Conditioners sold together by Branch R:

$360 - 108 = 252$

Let $R_{R}$ be the number of Refrigerators and $A_{R}$ be the number of Air Conditioners sold by Branch R.
Given that the difference between Refrigerators and Air Conditioners is 52:
$R_{R} - A_{R} = 52$