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 Refrigerators sold by Branch T is 33.33% more than the total number of Smart TVs sold by Branch R. If the total number of Air Conditioners sold by Branch T is two-fifths of the total number of Refrigerators sold by Branch S and the total number of appliances sold by Branch T is twice that of Branch P, then find the difference between the total number of Smart TVs sold by Branch T and the total number of Air Conditioners sold by Branch R.

The correct answer is 488.

Step 1: Analyze the data for the required branches (Branch R and Branch S).

For each branch, the total number of appliances sold includes Smart TVs, Refrigerators, and Air Conditioners.
Smart TVs sold = (Percentage of Smart TVs) × (Total appliances sold)
Remaining appliances (Refrigerators + Air Conditioners) = Total appliances sold - Smart TVs sold

Given that the number of Refrigerators sold is higher than the number of Air Conditioners sold by each branch, we have:
Refrigerators + Air Conditioners = Remaining appliances
Refrigerators - Air Conditioners = Given difference

Solving these two equations gives:

$\text{Refrigerators}=\frac{\text{Remaining appliances}+\text{Difference}}{2}$

$\text{Air Conditioners}=\frac{\text{Remaining appliances}-\text{Difference}}{2}$

Calculations for Branch R:
Total appliances sold by Branch R = 360
Smart TVs sold by Branch R = 30% of 360 =
$\frac{30}{100}\times 360=108$
Remaining appliances (Refrigerators + Air Conditioners) = 360 - 108 = 252
Difference between Refrigerators and Air Conditioners for Branch R = 52

Therefore:
Air Conditioners sold by Branch R =
$\frac{252-52}{2}=\frac{200}{2}=100$

Calculations for Branch S:
Total appliances sold by Branch S = 280
Smart TVs sold by Branch S = 15% of 280 =
$\frac{15}{100}\times 280=42$
Remaining appliances (Refrigerators + Air Conditioners) = 280 - 42 = 238
Difference between Refrigerators and Air Conditioners for Branch S = 102

Therefore:
Refrigerators sold by Branch S =
$\frac{238+102}{2}=\frac{340}{2}=170$

Step 2: Calculate the values for Branch T based on the given conditions.

1. Total appliances sold by Branch T is twice that of Branch P:
Total appliances sold by Branch P = 400
Total appliances sold by Branch T = 2 × 400 = 800

2. Total number of Refrigerators sold by Branch T is 33.33% (which equals
$\frac{1}{3}$
) more than the Smart TVs sold by Branch R:
Smart TVs sold by Branch R = 108
Refrigerators sold by Branch T =
$108+\left(\frac{1}{3}\times 108\right)=108+36=144$

3. Total number of Air Conditioners sold by Branch T is
$\frac{2}{5}$
of the total number of Refrigerators sold by Branch S:
Refrigerators sold by Branch S = 170
Air Conditioners sold by Branch T =
$\frac{2}{5}\times 170=68$

4. Total number of Smart TVs sold by Branch T:
Smart TVs (Branch T) = Total appliances (Branch T) - [Refrigerators (Branch T) + Air Conditioners (Branch T)]
Smart TVs (Branch T) = 800 - (144 + 68) = 800 - 212 = 588

Step 3: Calculate the required difference.

Difference = (Smart TVs sold by Branch T) - (Air Conditioners sold by Branch R)
Difference = 588 - 100 = 488

Thus, the required difference is 488.