Quantity I: The average age of 10 men is 30 years. If 5 more men join the group, the new average becomes 28 years. Find the average age of the 5 new men.

Quantity II: The average score of 20 students in a test is 65. If the top 5 scorers have an average score of 80, then find the average score of the remaining 15 students.

In the given question, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option. (Compare only numeric values)

The correct option is Quantity I < Quantity II.

Let us break down and solve each quantity step-by-step.

Step 1: Calculate Quantity I

We are given:
- Initial number of men = 10
- Initial average age of 10 men = 30 years

First, calculate the total age of the initial 10 men:

$\text{Total age of 10 men}=10\times 30=300\text{years}$

When 5 more men join the group:
- New total number of men = 10 + 5 = 15
- New average age = 28 years

Now, calculate the new total age of all 15 men:

$\text{Total age of 15 men}=15\times 28=420\text{years}$

Next, find the sum of the ages of the 5 new men by taking the difference between the total age of 15 men and 10 men:

$\text{Sum of ages of 5 new men}=420-300=120\text{years}$

Finally, calculate the average age of the 5 new men:

$\text{Average age of 5 new men}=\frac{120}{5}=24\text{years}$

Therefore, Quantity I = 24.

Step 2: Calculate Quantity II

We are given:
- Total number of students = 20
- Average score of 20 students = 65

First, calculate the total score of all 20 students:

$\text{Total score of 20 students}=20\times 65=1300$

Next, we are given:
- Number of top scorers = 5
- Average score of top 5 scorers = 80

Calculate the total score of the top 5 scorers:

$\text{Total score of top 5 scorers}=5\times 80=400$

Now, calculate the total score of the remaining 15 students (20 - 5 = 15):

$\text{Total score of remaining 15 students}=1300-400=900$

Finally, find the average score of the remaining 15 students:

$\text{Average score of remaining 15 students}=\frac{900}{15}=60$

Therefore, Quantity II = 60.

Step 3: Compare Quantity I and Quantity II

Comparing the numerical values obtained:
Quantity I = 24
Quantity II = 60

Since 24 < 60, we have Quantity I < Quantity II.