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

The total number of Smart TVs and Refrigerators sold by Branch P is how much more or less than half of the total number of Refrigerators sold by Branch Q and Branch S combined?

The correct answer is 55.

Step-by-step Explanation:

1. Calculations for Branch P:
Total number of appliances sold by Branch P = 400
Percentage of Smart TVs sold = 25%

Number of Smart TVs sold by Branch P:

$\text{Smart TVs}=25\%\text{of}400=\frac{25}{100}\times 400=100$

Total number of Refrigerators and Air Conditioners sold by Branch P:

$400-100=300$

We are given that the number of Refrigerators sold is higher than Air Conditioners, and their difference is 70:
Refrigerators + Air Conditioners = 300
Refrigerators - Air Conditioners = 70

Adding the two equations:

$2\times \text{Refrigerators}=300+70=370$

Number of Refrigerators sold by Branch P:

$\text{Refrigerators}=\frac{370}{2}=185$

Total number of Smart TVs and Refrigerators sold by Branch P combined:

$100+185=285$

2. Calculations for Branch Q:
Total number of appliances sold by Branch Q = 550
Percentage of Smart TVs sold = 10%

Number of Smart TVs sold by Branch Q:

$\text{Smart TVs}=10\%\text{of}550=\frac{10}{100}\times 550=55$

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

$550-55=495$

Difference between Refrigerators and Air Conditioners sold by Branch Q = 85:
Refrigerators + Air Conditioners = 495
Refrigerators - Air Conditioners = 85

Adding the two equations:

$2\times \text{Refrigerators}=495+85=580$

Number of Refrigerators sold by Branch Q:

$\text{Refrigerators}=\frac{580}{2}=290$

3. Calculations for Branch S:
Total number of appliances sold by Branch S = 280
Percentage of Smart TVs sold = 15%

Number of Smart TVs sold by Branch S:

$\text{Smart TVs}=15\%\text{of}280=\frac{15}{100}\times 280=42$

Total number of Refrigerators and Air Conditioners sold by Branch S:

$280-42=238$

Difference between Refrigerators and Air Conditioners sold by Branch S = 102:
Refrigerators + Air Conditioners = 238
Refrigerators - Air Conditioners = 102

Adding the two equations:

$2\times \text{Refrigerators}=238+102=340$

Number of Refrigerators sold by Branch S:

$\text{Refrigerators}=\frac{340}{2}=170$

4. Combined Refrigerators sold by Branch Q and Branch S:

$\text{Total Refrigerators (Q + S)}=290+170=460$

Half of the total Refrigerators sold by Branch Q and Branch S combined:

$\text{Half of Total}=\frac{460}{2}=230$

5. Finding the Required Difference:
Difference between the Smart TVs and Refrigerators sold by Branch P (285) and half of the total Refrigerators sold by Branch Q and Branch S combined (230):

$\text{Difference}=285-230=55$

Therefore, the required value is 55.