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 ratio of defective to non-defective Smart TVs sold by Branch S is 3:4, respectively. The number of defective Refrigerators sold by Branch S is three times more than the number of defective Smart TVs sold. Find the total number of non-defective Smart TVs and Refrigerators sold by Branch S.

The correct answer is 122.

Step-by-step Explanation:

From the given table, for Branch S:
- Total number of appliances sold = 280
- Percentage of Smart TVs sold = 15%
- Difference between Refrigerators and Air Conditioners sold = 102 (with Refrigerators > Air Conditioners)

Step 1: Find the total number of Smart TVs sold by Branch S

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

Step 2: Find the number of defective and non-defective Smart TVs sold by Branch S
The ratio of defective to non-defective Smart TVs sold by Branch S is given as 3 : 4.

$\text{Total ratio parts}=3+4=7$

$\text{Value of 1 part}=\frac{42}{7}=6$

$\text{Number of defective Smart TVs}=3\times 6=18$

$\text{Number of non-defective Smart TVs}=4\times 6=24$

Step 3: Find the total number of Refrigerators sold by Branch S
The remaining appliances sold by Branch S consist of Refrigerators and Air Conditioners:

$\text{Refrigerators}+\text{Air Conditioners}=280-42=238$

We are given that the number of Refrigerators sold is higher than Air Conditioners sold, and their difference is 102:

$\text{Refrigerators}-\text{Air Conditioners}=102$

Adding the two equations:

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

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

Step 4: Find the number of non-defective Refrigerators sold by Branch S
The number of defective Refrigerators sold is 3 times more than the number of defective Smart TVs sold.

$\text{Number of defective Refrigerators}=18+(3\times 18)=4\times 18=72$

$\text{Number of non-defective Refrigerators}=170-72=98$

Step 5: Calculate the total number of non-defective Smart TVs and Refrigerators sold by Branch S

$\text{Total non-defective appliances}=24+98=122$