Directions: Compare the numerical values of Quantity I and Quantity II based on the given information and select the appropriate option.

Quantity I: A container holds 80 liters of a solution containing orange concentrate and water in the ratio 5:3. If 24 liters of this solution is drawn out and replaced with pure water, and the final solution is sold at $15 per liter while pure orange concentrate costs $32 per liter, calculate the profit (in $) made on selling the mixture.

Quantity II: A trader mixes two varieties of coffee beans costing $18 per kg and $26 per kg in the ratio 3:1 respectively. Find the cost price (in $) per kg of the resulting coffee blend.

Correct Answer: Quantity I > Quantity II

Calculating Quantity I:
We are given that a container holds 80 liters of a solution containing orange concentrate and water in the ratio 5:3.
Total ratio parts:

$5+3=8$
Initial volume of orange concentrate:

$80\times \frac{5}{8}=50\text{liters}$
Initial volume of water:

$80\times \frac{3}{8}=30\text{liters}$

When 24 liters of the mixture is removed:
Orange concentrate removed:

$24\times \frac{5}{8}=15\text{liters}$
Water removed:

$24\times \frac{3}{8}=9\text{liters}$

Remaining orange concentrate:

$50-15=35\text{liters}$
Remaining water:

$30-9=21\text{liters}$

When 24 liters of pure water is added to replace the drawn solution:
Total final water volume:

$21+24=45\text{liters}$
Total final solution volume = 80 liters ($35+45=80\text{liters}$).

Cost Price (CP) of the mixture (cost of 35 liters of orange concentrate at $32 per liter):

$\text{CP}=35\times 32=\$1120$

Selling Price (SP) of 80 liters of the final solution at $15 per liter:

$\text{SP}=80\times 15=\$1200$

Profit made on selling the mixture:

$\text{Profit}=\text{SP}-\text{CP}=1200-1120=\$80$
Therefore, Quantity I = 80.

Calculating Quantity II:
Two varieties of coffee beans costing $18 per kg and $26 per kg are mixed in the ratio 3:1.
Cost price per kg of the resulting coffee blend:

$\text{Cost Price per kg}=\frac{3\times 18+1\times 26}{3+1}$

$\text{Cost Price per kg}=\frac{54+26}{4}=\frac{80}{4}=\$20$
Therefore, Quantity II = 20.

Comparison:
Comparing the numerical values of Quantity I and Quantity II:

$80>20$
Hence, Quantity I > Quantity II.