Quantity I: Present age of Randy, if 10 years are subtracted from the present age of Randy, then you would get twelve times of the present age of his grandson Sandy and Sandy is 19 years younger to Sundar whose age 24.
Quantity II: Average age of the remaining persons in the group if average age of group of 14 persons is 27 years and 9 months. two persons, each 42 years old, left the group.

Options

A. Quantity I ` gt` Quantity II
B. Quantity I `lt` Quantity II
C. Quantity I `ge `Quantity II
D. Quantity I `le` QuantityII

Answer

Let's break down the solution step by step for the given question.

### Quantity I: Present Age of Randy

1. **Identify the variables**:
- Let Randy's present age be \( x \).
- Sandy's age is given as 19 years younger than Sundar, whose age is 24. Therefore, Sandy's age can be calculated as:
\[ \text{Sandy's age} = 24 - 19 = 5 \text{ years} \]

2. **Set up the equation**:
- According to the problem, if 10 years are subtracted from Randy's age, it equals 12 times Sandy's age:
\[ x - 10 = 12 \times 5 \]

3. **Calculate the right side**:
- Calculate \( 12 \times 5 \):
\[ 12 \times 5 = 60 \]

4. **Formulate the equation**:
- Now substitute back into the equation:
\[ x - 10 = 60 \]

5. **Solve for \( x \)**:
- Add 10 to both sides:
\[ x = 60 + 10 = 70 \]

6. **Conclusion for Quantity I**:
- Randy's present age is \( 70 \) years.

### Quantity II: Average Age of Remaining Persons in the Group

1. **Calculate total age of the group**:
- The average age of 14 persons is given as 27 years and 9 months. Convert this into years:
\[ 27 \text{ years} + \frac{9}{12} \text{ years} = 27 + 0.75 = 27.75 \text{ years} \]
- Total age of the group:
\[ \text{Total age} = 14 \times 27.75 = 387 \text{ years} \]

2. **Subtract the ages of the two persons who left**:
- Two persons, each 42 years old, left the group. Their total age is:
\[ 2 \times 42 = 84 \text{ years} \]
- New total age of the group:
\[ \text{New total age} = 387 - 84 = 303 \text{ years} \]

3. **Calculate the new average age**:
- After the two persons left, the number of persons in the group is \( 14 - 2 = 12 \).
- New average age:
\[ \text{New average age} = \frac{303}{12} = 25.25 \text{ years} \]

4. **Conclusion for Quantity II**:
- The average age of the remaining persons in the group is \( 25.25 \) years.

### Final Comparison

- Quantity I (Randy's age): \( 70 \) years
- Quantity II (Average age of remaining persons): \( 25.25 \) years

### Conclusion
- Since \( 70 > 25.25 \), **Quantity I is greater than Quantity II**.