Directions: Determine the relationship between Quantity I and Quantity II based on the given information and select the appropriate option.

Quantity I: A factory initially employs 12 workers with a mean daily output of 45 units per worker. When 4 additional workers join the team, the overall average daily output increases to 50 units per worker. Find the average daily output of the 4 new workers.

Quantity II: A library has 25 shelves with an average of 70 books per shelf. If the 5 largest shelves hold an average of 110 books each, find the average number of books on the remaining 20 shelves.

Correct Answer: Quantity I > Quantity II

To determine the relationship between Quantity I and Quantity II, we calculate the required values step-by-step.

Step 1: Calculate Quantity I

Initially, there are 12 workers with an average daily output of 45 units per worker.

The total daily output of the initial 12 workers is:

$\text{Initial Output}=12\times 45=540\text{units}$

When 4 additional workers join, the total number of workers becomes:

$12+4=16\text{workers}$

The overall average daily output increases to 50 units per worker for all 16 workers.

The new total daily output of 16 workers is:

$\text{New Total Output}=16\times 50=800\text{units}$

The total daily output produced specifically by the 4 new workers is:

$\text{Output of 4 new workers}=800-540=260\text{units}$

The average daily output per worker among the 4 new workers is:

$\text{Quantity I}=\frac{260}{4}=65\text{units}$

Thus, Quantity I = 65.

Step 2: Calculate Quantity II

The library has 25 shelves with an average of 70 books per shelf.

The total number of books across all 25 shelves is:

$\text{Total Books}=25\times 70=1750\text{books}$

The 5 largest shelves hold an average of 110 books each.

The total number of books on these 5 largest shelves is:

$\text{Books on 5 largest shelves}=5\times 110=550\text{books}$

The remaining number of shelves is:

$25-5=20\text{shelves}$

The total number of books on the remaining 20 shelves is:

$\text{Books on remaining 20 shelves}=1750-550=1200\text{books}$

The average number of books per shelf on the remaining 20 shelves is:

$\text{Quantity II}=\frac{1200}{20}=60\text{books}$

Thus, Quantity II = 60.

Step 3: Comparison

Comparing the values obtained for both quantities:

$\text{Quantity I}=65$

$\text{Quantity II}=60$

Since 65 > 60, we conclude that Quantity I > Quantity II.