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

Calculate the ratio between the total number of Air Conditioners sold by Branch P and Branch Q combined to the total number of Smart TVs sold by Branch R and Branch S combined.

The correct answer is 32:15.

Step 1: Calculate the number of Air Conditioners sold by Branch P

Total appliances sold by Branch P = 400

Percentage of Smart TVs sold by Branch P = 25%

$\text{Number of Smart TVs (Branch P)}=25\%\times 400=100$

Remaining appliances (Refrigerators + Air Conditioners) sold by Branch P =

$400-100=300$

We are given that the difference between the number of Refrigerators and Air Conditioners sold by Branch P is 70, with Refrigerators being higher than Air Conditioners:

$\text{Refrigerators}+\text{Air Conditioners}=300$

$\text{Refrigerators}-\text{Air Conditioners}=70$

Subtracting the second equation from the first equation:

$2\times \text{Air Conditioners}=300-70=230$

$\text{Air Conditioners (Branch P)}=\frac{230}{2}=115$

Step 2: Calculate the number of Air Conditioners sold by Branch Q

Total appliances sold by Branch Q = 550

Percentage of Smart TVs sold by Branch Q = 10%

$\text{Number of Smart TVs (Branch Q)}=10\%\times 550=55$

Remaining appliances (Refrigerators + Air Conditioners) sold by Branch Q =

$550-55=495$

Given that the difference between Refrigerators and Air Conditioners sold by Branch Q is 85:

$2\times \text{Air Conditioners}=495-85=410$

$\text{Air Conditioners (Branch Q)}=\frac{410}{2}=205$

Step 3: Calculate the total number of Air Conditioners sold by Branch P and Branch Q combined

$\text{Total Air Conditioners (P + Q)}=115+205=320$

Step 4: Calculate the total number of Smart TVs sold by Branch R and Branch S combined

Number of Smart TVs sold by Branch R =

$30\%\times 360=108$

Number of Smart TVs sold by Branch S =

$15\%\times 280=42$

$\text{Total Smart TVs (R + S)}=108+42=150$

Step 5: Calculate the required ratio

The ratio of Air Conditioners sold by Branch P and Q combined to Smart TVs sold by Branch R and S combined is:

$\text{Required Ratio}=320:150=32:15$

Thus, the required ratio is 32:15.